\(1) \ 5(x - y) - y(x - y) = (x - y)(5 - y)\)

\(2) \ x(y + 1) + 8(y + 1) = (y + 1)(x + 8)\)

\(3) \ 5(x - y) - x(x - y) = (x - y)(5 - x)\)

\(4) \ z(x + y) - 5(x + y) = (x + y)(z - 5)\)

\(5) \ 3x(x + 5) - 2(5 + x) = (x + 5)(3x - 2)\)

\(6) \ x^2(x - 1) + 4(x - 1) = (x - 1)(x^2 + 4)\)

\(7) \ 5x(x - 1) - (1 - x) = 5x(x - 1) + (x - 1) = (x - 1)(5x + 1)\)

\(8) \ x(y - 1) - y(1 - y) = x(y - 1) + y(y - 1) = (y - 1)(x + y)\)

\(9) \ y(x - 2) - 3(2 - x) = y(x - 2) + 3(x - 2) = (x - 2)(y + 3)\)

\(10) \ 3(x - y) - y(y - x) = 3(x - y) + y(x - y) = (x - y)(3 + y)\)

\(11) \ 3x(x - 2) + 5(2 - x) = 3x(x - 2) - 5(x - 2) = (x - 2)(3x - 5)\)

\(12) \ 7x(x - y) - (y - x) = 7x(x - y) + (x - y) = (x - y)(7x + 1)\)

\(13) \ 3x(x - 1) - 2y(1 - x) = 3x(x - 1) + 2y(x - 1) = (x - 1)(3x + 2y)\)

\(14) \ 3(x - y) - 5x(y - x) = 3(x - y) + 5x(x - y) = (x - y)(3 + 5x)\)

\(15) \ x(x - y) + y(y - x) = x(x - y) - y(x - y) = (x - y)(x - y) = (x - y)^2\)

\(16)\ x(y^2-1)+4(1-y^2)=x(y^2-1)-4(y^2-1)\)

\(=(y^2-1)(x-4)=(y-1)(y+1)(x-4)\)

\(17) \ x(2y - 1) - 5(2y - 1) = (2y - 1)(x - 5)\)

\(18) \ 9(x - 2y) + x(2y - x) = 9(x - 2y) - x(x - 2y) = (x - 2y)(9 - x)\)

\(19) \ 10x(x - y) - 8y(y - x) = 10x(x - y) + 8y(x - y) = 2(x - y)(5x + 4y)\)

\(20) \ 3x(x - y) + 6(y - x) = 3x(x - y) - 6(x - y) = 3(x - y)(x - 2)\)

\(21) \ 5x(x - 1) - 15x(1 - x) = 5x(x - 1) + 15x(x - 1) = 20x(x - 1)\)

\(22) \ 10x(x - y) - 6y(y - x) = 10x(x - y) + 6y(x - y) = 2(x - y)(5x + 3y)\)

\(23)\ 3x(x-2y)+6y(2y-x)=3x(x-2y)-6y(x-2y)\)

\(=3(x-2y)(x-2y)=3(x-2y)^2\)

\(24) \ 20x(x + y) - 8y(y + x) = 4(x + y)(5x - 2y)\)

\(25)\ xy^2(x-3)+4x(3-x)=xy^2(x-3)-4x(x-3)\)

\(=x(x-3)(y^2-4)=x(x-3)(y-2)(y+2)\)

\(26) \ 2x(x + y) - 6x^2(x + y) = 2x(x + y)(1 - 3x)\)

\(27) \ 9x^2(y + z) + 3x(y + z) = 3x(y + z)(3x + 1)\)

\(28) \ 2x^2(y - 1) - 2x(y - 1) = 2x(y - 1)(x - 1)\)

\(29)\ 10xy(x-y)-6y(y-x)\)

\(=10xy(x-y)+6y(x-y)=2y(x-y)(5x+3)\)

1: 5(x-y)-y(x-y)

=(x-y)(5-y)

2: x(y+1)+8(y+1)=(x+8)(y+1)

3: 5(x-y)-x(x-y)

=(x-y)(5-x)

4: z(x+y)-5(x+y)

=(x+y)(z-5)

5: 3x(x+5)-2(5+x)

=3x(x+5)-2(x+5)

=(x+5)(3x-2)

6: \(x^2\left(x-1\right)+4\left(x-1\right)=\left(x-1\right)\left(x^2+4\right)\)

7: 5x(x-1)-(1-x)

=5x(x-1)+(x-1)

=(x-1)(5x+1)

8: x(y-1)-y(1-y)

=x(y-1)+y(y-1)

=(y-1)(x+y)

9: y(x-2)-3(2-x)

=y(x-2)+3(x-2)

=(x-2)(y+3)

10: 3(x-y)-y(y-x)

=3(x-y)+y(x-y)

=(x-y)(y+3)

11: 3x(x-2)+5(2-x)

=3x(x-2)-5(x-2)

=(x-2)(3x-5)

12: 7x(x-y)-(y-x)

=7x(x-y)+(x-y)

=(x-y)(7x+1)

13: \(3x\left(x-1\right)-2y\left(1-x\right)\)

=3x(x-1)+2y(x-1)

=(x-1)(3x+2y)

14: 3(x-y)-5x(y-x)

=3(x-y)+5x(x-y)

=(x-y)(5x+3)

15: x(x-y)+y(y-x)

=x(x-y)-y(x-y)

=(x-y)(x-y)

\(=\left(x-y\right)^2\)

16: \(x\left(y^2-1\right)+4\left(1-y^2\right)=x\left(y^2-1\right)-4\left(y^2-1\right)\)

\(=\left(x-4\right)\left(y^2-1\right)=\left(x-4\right)\left(y-1\right)\left(y+1\right)\)

17: x(2y-1)-5(2y-1)=(2y-1)(x-5)

18: 9(x-2y)+x(2y-x)

=9(x-2y)-x(x-2y)

=(x-2y)(9-x)

19: 10x(x-y)-8y(y-x)

=10x(x-y)+8y(x-y)

=(x-y)(10x+8y)

=2(5x+4y)(x-y)

20: 3x(x-y)+6(y-x)

=3x(x-y)-6(x-y)

=(x-y)(3x-6)

=3(x-2)(x-y)

21: 5x(x-1)-15x(1-x)

=5x(x-1)+15x(x-1)

=20x(x-1)

22: 10x(x-y)-6y(y-x)

=10x(x-y)+6y(x-y)

=(x-y)(10x+6y)

=2(5x+3y)(x-y)

23: 3x(x-2y)+6y(2y-x)

=(3x-6y)(x-2y)

\(=3\left(x-2y\right)^2\)

24: 20x(x+y)-8y(y+x)

=20x(x+y)-8y(x+y)

=(x+y)(20x-8y)

=4(5x-2y)(x+y)

25: \(xy^2\left(x-3\right)+4x\left(3-x\right)=\left(x-3\right)\left(xy^2-4x\right)\)

\(=x\left(x-3\right)\cdot\left(y^2-4\right)\)

=x(x-3)(y-2)(y+2)

26: \(2x\left(x+y\right)-6x^2\left(x+y\right)\)

\(=\left(x+y\right)\left(2x-6x^2\right)\)

\(=2x\left(1-3x\right)\left(x+y\right)\)

27: \(9x^2\left(y+z\right)+3x\left(y+z\right)\)

\(=\left(y+z\right)\left(9x^2+3x\right)\)

=3x(3x+1)(y+z)

28: \(2x^2\left(y-1\right)-2x\left(y-1\right)\)

\(=\left(y-1\right)\left(2x^2-2x\right)\)

=2x(x-1)(y-1)

29: \(10xy\left(x-y\right)-6y\left(y-x\right)\)

=10xy(x-y)+6y(x-y)

=(x-y)(10xy+6y)

=2y(5x+3)(x-y)

1. 5(x - y) - y(x - y) Có nhân tử chung là (x - y) nên ta đặt ra ngoài: = (x - y)(5 - y) 2. x(y + 1) + 8(y + 1) Có nhân tử chung là (y + 1) nên ta đặt ra ngoài: = (y + 1)(x + 8) 3. 5(x - y) - x(x - y) Có nhân tử chung là (x - y) nên ta đặt ra ngoài: = (x - y)(5 - x) 4. z(x + y) - 5(x + y) Có nhân tử chung là (x + y) nên ta đặt ra ngoài: = (x + y)(z - 5)

\(1) \ x^2 - x = x(x - 1)\)

\(2) \ x^2 - 8x = x(x - 8)\)

\(3) \ x^2 + 12x = x(x + 12)\)

\(4) \ x^3 - 4x = x(x^2 - 4) = x(x - 2)(x + 2)\)

\(5) \ 3x^2 - x = x(3x - 1)\)

\(6) \ 2xy + y^2 = y(2x + y)\)

\(7) \ x^2 - xy = x(x - y)\)

\(8) \ x^3 - x^2y = x^2(x - y)\)

\(9) \ 3x - 3y = 3(x - y)\)

\(10) \ 10x + 15y = 5(2x + 3y)\)

\(11) \ 3x - 12y = 3(x - 4y)\) '

\(12) \ 4x - 20 = 4(x - 5)\)

\(13) \ 6x - 2x^2 = 2x(3 - x)\)

\(14) \ 2x - 4x^2 = 2x(1 - 2x)\)

\(15) \ 3x^2 - 6x = 3x(x - 2)\)

\(16) \ 3x^2 + 6x = 3x(x + 2)\)

\(17) \ 4x^2 + 6x = 2x(2x + 3)\)

\(18) \ 2x^2 + 6x = 2x(x + 3)\)

\(19) \ 2x^3 - 8x = 2x(x^2 - 4) = 2x(x - 2)(x + 2)\)

\(20) \ 2x^3 - 3x^2 = x^2(2x - 3)\)

\(21) \ 3x^4 - 24x = 3x(x^3 - 8) = 3x(x - 2)(x^2 + 2x + 4)\)

\(22) \ 4x^2 - 12x = 4x(x - 3)\)

\(23) \ 6x^3 + 9x^2 = 3x^2(2x + 3)\)

\(24) \ 9x - 16x^2 = x(9 - 16x)\)

\(25) \ yx^3 + 8y = y(x^3 + 8) = y(x + 2)(x^2 - 2x + 4)\)

\(26) \ x^3y + 5x^2y = x^2y(x + 5)\)

\(27) \ xy^2 - 25x = x(y^2 - 25) = x(y - 5)(y + 5)\)

\(28) \ 7x^2 + 14xy = 7x(x + 2y)\)

\(29) \ 4x^2y - 6xy^2 = 2xy(2x - 3y)\)

\(30) \ 3xy - 9x^2 = 3x(y - 3x)\)

\(31) \ 6x^2 - 3xy = 3x(2x - y)\)

\(32) \ 3xy^2 - 3x^3 = 3x(y^2 - x^2) = 3x(y - x)(y + x)\)

\(33) \ 3xy + 6xz = 3x(y + 2z)\)

\(34) \ 18x^2y - 12x^3 = 6x^2(3y - 2x)\)

\(35) \ 8xy^2 - 2x^2y = 2xy(4y - x)\)

\(36) \ 3xy^2 + 6xyz = 3xy(y + 2z)\)

1: \(x^2-x=x\cdot x-x\cdot1=x\left(x-8\right)\)

2: \(x^2-8x=x\cdot x-x\cdot8=x\left(x-8\right)\)

3: \(x^2+12x=x\cdot x+x\cdot12=x\left(x+12\right)\)

4: \(x^3-4x\)

\(=x\left(x^2-4\right)=x\left(x-2\right)\left(x+2\right)\)

5: \(3x^2-x=x\cdot3x-x\cdot1=x\left(3x-1\right)\)

6: \(2xy+y^2=y\cdot2x+y\cdot y=y\left(2x+y\right)\)

7: \(x^2-xy=x\cdot x-x\cdot y=x\left(x-y\right)\)

8: \(x^3-x^2y=x^2\cdot x-x^2\cdot y=x^2\left(x-y\right)\)

9: \(3x-3y=3\left(x-y\right)\)

10: 10x+15y=5(2x+3y)

11: \(3x-12y=3\cdot x-3\cdot4y=3\left(x-4y\right)\)

12: \(4x-20=4\cdot x-4\cdot5=4\left(x-5\right)\)

13: \(6x-2x^2=2x\cdot3-2x\cdot x=2x\left(3-x\right)\)

14: \(2x-4x^2=2x\cdot1-2x\cdot2x=2x\left(1-2x\right)\)

15: \(3x^2-6x=3x\cdot x-3x\cdot2=3x\left(x-2\right)\)

16: \(3x^2+6x=3x\cdot x+3x\cdot2=3x\left(x+2\right)\)

17: \(4x^2+6x=2x\cdot2x+2x\cdot3=2x\left(2x+3\right)\)

18: \(2x^2+6x=2x\cdot x+2x\cdot3=2x\left(x+3\right)\)

19: \(2x^3-8x=2x\left(x^2-4\right)=2x\left(x-2\right)\left(x+2\right)\)

20: \(2x^3-3x^2=x^2\cdot2x-x^2\cdot3=x^2\left(2x-3\right)\)

21: \(3x^4-24x\)

\(=3x\left(x^3-8\right)=3x\left(x-2\right)\left(x^2+2x+4\right)\)

22: \(4x^2-12x=4x\cdot x-4x\cdot3=4x\left(x-3\right)\)

23: \(6x^3+9x^2=3x^2\cdot2x+3x^2\cdot3=3x^2\left(2x+3\right)\)

24: \(9x-16x^2=x\cdot9-x\cdot16x=x\left(9-16x\right)\)

25: \(x^3y+8y=y\left(x^3+8\right)=y\left(x+2\right)\left(x^2-2x+4\right)\)

26: \(x^3y+5x^2y=x^2y\cdot x+x^2y\cdot5=x^2y\left(x+5\right)\)

27: \(xy^2-25x=x\left(y^2-25\right)=x\left(y-5\right)\left(y+5\right)\)

28: \(7x^2+14xy=7x\cdot x+7x\cdot2y=7x\left(x+2y\right)\)

29: \(4x^2y-6xy^2=2xy\cdot2x-2xy\cdot3y=2xy\left(2x-3y\right)\)

30: \(3xy-9x^2=3x\cdot y-3x\cdot3x=3x\left(y-3x\right)\)

31: \(6x^2-3xy=3x\cdot2x-3x\cdot y=3x\left(2x-y\right)\)

32: \(3xy^2-3x^3=3x\left(y^2-x^2\right)=3x\left(y-x\right)\left(y+x\right)\)

33: 3xy+6xz=3x(y+2z)

34: \(18x^2y-12x^3=6x^2\left(3y-2x\right)\)

35: \(8xy^2-2x^2y=2xy\cdot4y-2xy\cdot x=2xy\left(4y-x\right)\)

36: \(3xy^2+6xyz=3xy\cdot y+3xy\cdot2z=3xy\left(y+2z\right)\)

1. x^2 - x = x(x - 1) 2. x^2 - 8x = x(x - 8) 3. x^2 + 12x = x(x + 12) 4. x^3 - 4x = x(x^2 - 4) = x(x - 2)(x + 2) 5. 3x^2 - x = x(3x - 1) 6. 2xy + y^2 = y(2x + y) 7. x^2 - xy = x(x - y) 8. x^3 - x^2*y = x^2 * (x - y) 9. 3x - 3y = 3(x - y) 10. 10x + 15y = 5(2x + 3y) 11. 3x - 12y = 3(x - 4y) 12. 4x - 20 = 4(x - 5) 13. 6x - 2x^2 = 2x(3 - x) 14. 2x - 4x^2 = 2x(1 - 2x) 15. 3x^2 - 6x = 3x(x - 2) 16. 3x^2 + 6x = 3x(x + 2) 17. 4x^2 + 6x = 2x(2x + 3) 18. 2x^2 + 6x = 2x(x + 3) 19. 2x^3 - 8x = 2x(x^2 - 4) = 2x(x - 2)(x + 2) 20. 2x^3 - 3x^2 = x^2 * (2x - 3) 21. 3x^4 - 24x = 3x(x^3 - 8) = 3x(x - 2)(x^2 + 2x + 4) 22. 4x^2 - 12x = 4x(x - 3) 23. 6x^3 + 9x^2 = 3x^2 * (2x + 3) 24. 9x - 16x^2 = x(9 - 16x) 25. yx^3 + 8y = y(x^3 + 8) = y(x + 2)(x^2 - 2x + 4) 26. x^3y + 5x^2y = x^2*y * (x + 5) 27. xy^2 - 25x = x(y^2 - 25) = x(y - 5)(y + 5) 28. 7x^2 + 14xy = 7x(x + 2y) 29. 4x^2*y - 6xy^2 = 2xy(2x - 3y) 30. 3xy - 9x^2 = 3x(y - 3x) 31. 6x^2 - 3xy = 3x(2x - y) 32. 3xy^2 - 3x^3 = 3x(y^2 - x^2) = 3x(y - x)(y + x) 33. 3xy + 6xz = 3x(y + 2z) 34. 18x^2*y - 12x^3 = 6x^2 * (3y - 2x) 35. 8xy^2 - 2x^2*y = 2xy(4y - x) 36. 3xy^2 + 6xyz = 3xy(y + 2z)

a: \(3ab-b^2a-A=ab+b^2a\)

=>\(A=3ab-ab^2-ab-ab^2=2ab-2ab^2\)

b: \(2A+x^2+3x+1=3x^2-x+3\)

=>\(2A=3x^2-x+3-x^2-3x-1=2x^2-4x+2\)

=>\(A=x^2-2x+1\)

a) A = (3ab - b^2a) - (ab + b^2a) A = 3ab - b^2a - ab - b^2a A = (3ab - ab) + (-b^2a - b^2a) A = 2ab - 2b^2a b) 2A = (3x^2 - x + 3) - (x^2 + 3x + 1) 2A = 3x^2 - x + 3 - x^2 - 3x - 1 2A = (3x^2 - x^2) + (-x - 3x) + (3 - 1) 2A = 2x^2 - 4x + 2 A = (2x^2 - 4x + 2) : 2 A = x^2 - 2x + 1

Gọi N là trung điểm của HD

Xét ΔHDC có

M,N lần lượt là trung điểm của HC,HD

=>MN là đường trung bình của ΔHDC

=>MN//DC và \(MN=\frac{DC}{2}\)

MN//DC

DC⊥ AD

Do đó: MN⊥AD

Xét ΔAMD có

MN,DH là các đường cao

MN cắt DH tại N

Do đó: N là trực tâm của ΔAMD

=>AN⊥DM

MN//DC

DC//AB

Do đó: MN//AB

\(MN=\frac{DC}{2}\)

\(AB=\frac{DC}{2}\)

Do đó: MN=AB

Xét tứ giác ABMN có

AB//MN

AB=MN

Do đó: ABMN là hình bình hành

=>AN//BM

mà AN⊥DM

nên BM⊥MD

=>\(\hat{BMD}=90^0\)

Bài 1;

1; Đặt \(A=x\left(x+1\right)-\left(x+2\right)^2\)

\(=x^2+x-x^2-4x-4\)

=-3x-4

Khi x=1 thì \(A=-3\cdot1-4=-3-4=-7\)

2: Đặt B=(5x+2)(2x-7)-(2x+5)(2x-5)

\(=10x^2-35x+4x-14-\left(4x^2-25\right)\)

\(=10x^2-31x-14-4x^2+25=6x^2-31x+11\)

Khi x=-3 thì \(B=6\cdot\left(-3\right)^2-31\cdot\left(-3\right)+11\)

=54+93+11

=65+93

=158

3: Đặt \(C=\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)\)

\(=x^2-4x+4-\left(x^2-9\right)\)

\(=x^2-4x+4-x^2+9=-4x+13\)

Khi x=2 thì \(C=-4\cdot2+13=-8+13=5\)

BÀi 2:

1: \(\left(x+7\right)^2-x\left(x-3\right)=12\)

=>\(x^2+14x+49-x^2+3x=12\)

=>17x=12-49=-37

=>\(x=-\frac{37}{17}\)

2: \(\left(2x+3\right)^2-4x^2=10\)

=>\(4x^2+12x+9-4x^2=10\)

=>12x=10-9=1

=>\(x=\frac{1}{12}\)

3: \(\left(x+2\right)^2-\left(x-2\right)\left(x+1\right)=3\)

=>\(x^2+4x+4-\left(x^2-x-2\right)=3\)

=>\(x^2+4x+4-x^2+x+2=3\)

=>5x+5=3

=>5x=-2

=>\(x=-\frac25\)

4: \(\left(2x+3\right)^2-4\left(x-1\right)^2=2\)

=>\(4x^2+12x+9-4\left(x^2-2x+1\right)=2\)

=>\(4x^2+12x+9-4x^2+8x-4=2\)

=>20x+5=2

=>20x=-3

=>\(x=-\frac{3}{20}\)

5: \(\left(x-2\right)^2-\left(x+1\right)\left(x+3\right)=-7\)

=>\(x^2-4x+4-\left(x^2+4x+3\right)=-7\)

=>\(x^2-4x+4-x^2-4x-3=-7\)

=>-8x+1=-7

=>-8x=-8

=>x=1

6: \(\left(x+1\right)^2-\left(x-2\right)\left(x+2\right)=0\)

=>\(x^2+2x+1-\left(x^2-4\right)=0\)

=>\(x^2+2x+1-x^2+4=0\)

=>2x=-5

=>x=-5/2

7: \(\left(2x+3\right)^2-4\left(x-1\right)^2=16\)

=>\(4x^2+12x+9-4\left(x^2-2x+1\right)=16\)

=>\(4x^2+12x+9-4x^2+8x-4=16\)

=>20x+5=16

=>20x=11

=>\(x=\frac{11}{20}\)

8: \(\left(x-2\right)^2-x\left(x-5\right)-3=0\)

=>\(x^2-4x+4-x^2+5x-3=0\)

=>x+1=0

=>x=-1

9: \(\left(3x-2\right)^2-\left(x+9\right)\left(3x+2\right)=0\)

=>\(9x^2-12x+4-3x^2-2x-27x-18=0\)

=>\(6x^2-41x-14=0\)

\(\Delta=\left(-41\right)^2-4\cdot6\cdot\left(-14\right)=2017>0\)

Do đó: Phương trình có hai nghiệm phân biệt là:

\(\left[\begin{array}{l}x=\frac{41-\sqrt{2017}}{2\cdot6}=\frac{41-\sqrt{2017}}{12}\\ x=\frac{41+\sqrt{2017}}{2\cdot6}=\frac{41+\sqrt{2017}}{12}\end{array}\right.\)

X=0 y=3

x=0 y=3

BÀi 4:

1: \(x\left(1-x\right)+\left(x-1\right)^2\)

\(=x-x^2+x^2-2x+1\)

=-x+1

2: \(\left(x-3\right)^2-x^2+10x-7\)

\(=x^2-6x+9-x^2+10x-7\)

=4x+2

3: \(\left(x+2\right)^2-\left(x-3\right)\left(x+1\right)\)

\(=x^2+4x+4-\left(x^2-2x-3\right)\)

\(=x^2+4x+4-x^2+2x+3=6x+7\)

4: (x+4)(x-2)-\(\left(x-3\right)^2\)

\(=x^2-2x+4x-8-\left(x^2-6x+9\right)\)

\(=x^2+2x-8-x^2+6x-9=8x-17\)

5: \(\left(x-2\right)^2+\left(x-1\right)\left(x+5\right)\)

\(=x^2-4x+4+x^2+4x-5=2x^2-1\)

6: \(\left(x+3\right)\left(x-3\right)-x\left(x+23\right)\)

\(=x^2-9-x^2-23x\)

=-23x-9

Bài 3:

1: \(\left(2x+1\right)^2+\left(2x-1\right)^2\)

\(=4x^2-4x+1+4x^2+4x+1=8x^2+2\)

2: \(-\left(x+1\right)^2-\left(x-1\right)^2\)

\(=-\left(x^2+2x+1\right)-\left(x^2-2x+1\right)\)

\(=-x^2-2x-1-x^2+2x-1=-2x^2-2\)

3: \(\left(x+2y\right)^2-\left(x-2y\right)^2\)

\(=\left(x+2y-x+2y\right)\left(x+2y+x-2y\right)\)

\(=4y\cdot2x=8xy\)

4: \(\left(3x+y\right)^2+\left(x-y\right)^2\)

\(=9x^2+6xy+y^2+x^2-2xy+y^2=10x^2+4xy+2y^2\)

5: \(-\left(x+5\right)^2-\left(x-3\right)^2\)

\(=-\left(x^2+10x+25\right)-\left(x^2-6x+9\right)\)

\(=-x^2-10x-25-x^2+6x-9=-2x^2-4x-34\)

6: \(\left(3x-2\right)^2-\left(3x-1\right)^2\)

\(=\left(3x-2-3x+1\right)\left(3x-2+3x-1\right)=-1\left(6x-3\right)=-6x+3\)

7: \(\left(x-4y\right)^2+\left(x+4y\right)^2\)

\(=x^2-8xy+16y^2+x^2+8xy+16y^2=2x^2+32y^2\)

8: \(-\left(-2x+3\right)^2-\left(5x-3\right)^2\)

\(=-\left(4x^2-12x+9\right)-\left(25x^2-30x+9\right)\)

\(=-4x^2+12x-9-25x^2+30x-9=-29x^2+42x-18\)

9: \(\left(-2x+3\right)^2-\left(5x-3\right)^2\)

\(=4x^2-12x+9-\left(25x^2-30x+9\right)\)

\(=4x_{}^2-12x+9-25x^2+30x-9=-21x^2+18x\)

10: \(\left(2x+1\right)^2+\left(-3x-1\right)^2\)

\(=4x^2+4x+1+9x^2+6x+1=13x^2+10x+2\)

11: \(-\left(x-y\right)^2-\left(2x+y\right)^2\)

\(=-\left(x^2-2xy+y^2\right)-\left(4x^2+4xy+y^2\right)\)

\(=-x^2+2xy-y^2-4x^2-4xy-4y^2=-5x^2-2xy-5y^2\)

12: \(-\left(x+1\right)^2+\left(x-1\right)^2\)

\(=-x^2-2x-1+x^2-2x+1=-4x\)

13: \(\left(2x+7\right)^2+\left(-2x-3\right)^2\)

\(=4x^2+28x+49+4x_{}^2-12x+9=8x^2+16x+58\)

14: \(-\left(2x-y\right)^2-\left(x+3y\right)^2\)

\(=-\left(4x^2-4xy+y^2\right)-\left(x^2+6xy+9y^2\right)\)

\(=-4x^2+4xy-y^2-x^2-6xy-9y^2=-5x^2-2xy-10y^2\)

15: \(-\left(2x+7\right)^2+\left(-2x-3\right)^2\)

\(=-4x^2-28x-49+4x^2+12x+9=-16x-40\)

Bài 1:

1: \(\left(x+1\right)^2=x^2+2x+1\)

2: \(\left(4+x\right)^2=\left(x+4\right)^2=x^2+8x+16\)

3: \(\left(5x+1\right)^2=\left(5x\right)^2+2\cdot5x\cdot1+1^2=25x^2+10x+1\)

4: \(\left(2x+3\right)^2=\left(2x\right)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9\)

5: \(\left(x+2y\right)^2=x^2+2\cdot x\cdot2y+\left(2y\right)^2=x^2+4xy+4y^2\)

6: \(\left(x+5y\right)^2=x^2+2\cdot x\cdot5y+\left(5y\right)^2=x^2+10xy+25y^2\)

7: \(\left(3x+5y\right)^2=\left(3x\right)^2+2\cdot3x\cdot5y+\left(5y\right)^2=9x^2+30xy+25y^2\)

8: \(\left(2x+3y\right)^2=\left(2x\right)^2+2\cdot2x\cdot3y+\left(3y\right)^2=4x^2+12xy+9y^2\)

9: \(\left(x^2+9\right)^2=\left(x^2\right)^2+2\cdot x^2\cdot9+9^2=x^4+18x^2+81\)

10: \(\left(2x^2+1\right)^2=\left(2x^2\right)^2+2\cdot2x^2\cdot1+1^2=4x^4+4x^2+1\)

11: \(\left(x+2y^2\right)^2=x^2+2\cdot x\cdot2y^2+\left(2y^2\right)^2=x^2+4xy^2+4y^4\)

12: \(\left(2x+3y^2\right)^2=\left(2x\right)^2+2\cdot2x\cdot3y^2+\left(3y^2\right)^2\)

\(=4x^2+12xy^2+9y^4\)

Bài 2:

1: \(x^2-4=\left(x-2\right)\left(x+2\right)\)

2: \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)

3: \(4x^2-9=\left(2x\right)^2-3^2=\left(2x-3\right)\left(2x+3\right)\)

4: \(9-25x^2=3^2-\left(5x\right)^2=\left(3-5x\right)\left(3+5x\right)\)

5: \(4x^2-25=\left(2x\right)^2-5^2=\left(2x-5\right)\left(2x+5\right)\)

6: \(9x^2-36=9\left(x^2-4\right)=9\left(x-2\right)\left(x+2\right)\)

7: \(\left(3x\right)^2-y^2=\left(3x-y\right)\left(3x+y\right)\)

8: \(x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)

9: \(\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)

10: \(\left(3x\right)^2-9y^4=9x^2-9y^4=9\left(x^2-y^4\right)=9\left(x-y^2\right)\left(x+y^2\right)\)

11: \(16x^2-\left(y^2\right)^2=\left(4x\right)^2-\left(y^2\right)^2=\left(4x-y^2\right)\left(4x+y^2\right)\)

12: \(x^4-\left(3y^2\right)^2=\left(x^2\right)^2-\left(3y^2\right)^2=\left(x^2-3y^2\right)\left(x^2+3y^2\right)\)

13: \(\left(x-1\right)\left(x+1\right)=x^2-1^2=x^2-1\)

14: (x-5)(x+5)

\(=x^2-5^2=x^2-25\)

15: \(\left(x-6\right)\left(6+x\right)=x^2-6^2=x^2-36\)

16: (2x+1)(2x-1)=\(\left(2x\right)^2-1^2=4x^2-1\)

17: \(\left(x-2y\right)\left(2y+x\right)=\left(x-2y\right)\left(x+2y\right)=x^2-4y^2\)

18: (5x-3y)(3y+5x)

=(5x-3y)(5x+3y)

\(=\left(5x\right)^2-\left(3y\right)^2=25x^2-9y^2\)

19: \(\left(\frac{1}{x}-5\right)\left(\frac{1}{x}+5\right)=\left(\frac{1}{x}\right)^2-5^2=\frac{1}{x^2}-25\)

20: \(\left(x-\frac32\right)\left(x+\frac32\right)=x^2-\left(\frac32\right)^2=x^2-\frac94\)

21: \(\left(\frac{x}{3}-\frac{y}{4}\right)\left(\frac{x}{3}+\frac{y}{4}\right)=\left(\frac{x}{3}\right)^2-\left(\frac{y}{4}\right)^2=\frac{x^2}{9}-\frac{y^2}{16}\)

22: \(\left(\frac{x}{y}-\frac23\right)\left(\frac{x}{y}+\frac23\right)=\left(\frac{x}{y}\right)^2-\left(\frac23\right)^2=\frac{x^2}{y^2}-\frac49\)

23: \(\left(\frac{x}{2}+\frac{y}{3}\right)\left(\frac{y}{3}-\frac{x}{2}\right)=\left(\frac{y}{3}\right)^2-\left(\frac{x}{2}\right)^2=\frac{y^2}{9}-\frac{x^2}{4}\)

24: \(\left(2x-\frac23\right)\left(\frac23+2x\right)=\left(2x\right)^2-\left(\frac23\right)^2=4x^2-\frac49\)

25: \(\left(2x+\frac35\right)\left(\frac35-2x\right)=\left(\frac35+2x\right)\left(\frac35-2x\right)=\left(\frac35\right)^2-\left(2x\right)^2=\frac{9}{25}-4x^2\)

26: \(\left(\frac12x-\frac43\right)\left(\frac43+\frac12x\right)=\left(\frac12x\right)^2-\left(\frac43\right)^2=\frac14x^2-\frac{16}{9}\)

27: \(\left(\frac23x^2-\frac{y}{2}\right)\left(\frac23x^2+\frac{y}{2}\right)=\left(\frac23x^2\right)^2-\left(\frac{y}{2}\right)^2=\frac49x^4-\frac{y^2}{4}\)

28: \(\left(3x-y^2\right)\left(3x+y^2\right)=\left(3x\right)^2-\left(y^2\right)^2=9x^2-y^4\)

29: \(\left(x^2-2y\right)\left(x^2+2y\right)=\left(x^2\right)^2-\left(2y\right)^2=x^4-4y^2\)

30: \(\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x^2\right)^2-\left(y^2\right)^2=x^4-y^4\)

Bài 1:

1, \((x+1)^2 = x^2 + 2x + 1\)

2, \((4+x)^2 = 16 + 8x + x^2\)

3, \((5x+1)^2 = 25x^2 + 10x + 1\)

4, \((2x+3)^2 = 4x^2 + 12x + 9\)

5, \((x+2y)^2 = x^2 + 4xy + 4y^2\)

6, \((x+5y)^2 = x^2 + 10xy + 25y^2\)

7, \((3x+5y)^2 = 9x^2 + 30xy + 25y^2\)

8, \((2x+3y)^2 = 4x^2 + 12xy + 9y^2\)

9, \((x^2+9)^2 = x^4 + 18x^2 + 81\)

10, \((2x^2+1)^2 = 4x^4 + 4x^2 + 1\)

11, \((x+2y^2)^2 = x^2 + 4xy^2 + 4y^4\)

12, \(x^4 - (3y^2)^2 = (x^2-3y^2)(x^2+3y^2)\)

Bài 2:

Từ câu 1 đến câu 12 (Phân tích thành tích \((A-B)(A+B)\) )

1, \(x^2 - 4 = (x-2)(x+2)\)

2, \(1 - 4x^2 = (1-2x)(1+2x)\)

3, \(4x^2 - 9 = (2x-3)(2x+3)\)

4, \(9 - 25x^2 = (3-5x)(3+5x)\)

5, \(4x^2 - 25 = (2x-5)(2x+5)\)

6, \(9x^2 - 36 = (3x-6)(3x+6) = 9(x-2)(x+2)\)

7, \((3x)^2 - y^2 = (3x-y)(3x+y)\)

8, \(x^2 - (2y)^2 = (x-2y)(x+2y)\)

9, \((2x)^2 - y^2 = (2x-y)(2x+y)\)

10, \((3x)^2 - 9y^4 = (3x-3y^2)(3x+3y^2)\)

11, \(16x^2 - (y^2)^2 = (4x-y^2)(4x+y^2)\)

12, \(x^4 - (3y^2)^2 = (x^2-3y^2)(x^2+3y^2)\)

Từ câu 13 đến câu 30 (Triển khai thành hiệu \(A^2 - B^2\) ):

13, \((x-1)(x+1) = x^2 - 1\)

14, \((x-5)(x+5) = x^2 - 25\)

15, \((x-6)(6+x) = x^2 - 36\)

16, \((2x+1)(2x-1) = 4x^2 - 1\)

17, \((x-2y)(2y+x) = x^2 - 4y^2\)

18, \((5x-3y)(3y+5x) = 25x^2 - 9y^2\)

19, \(\left(\frac{1}{x}-5\right)\left(\frac{1}{x}+5\right) = \frac{1}{x^2} - 25\)

20, \(\left(x-\frac{3}{2}\right)\left(x+\frac{3}{2}\right) = x^2 - \frac{9}{4}\)

21, \(\left(\frac{x}{3}-\frac{y}{4}\right)\left(\frac{x}{3}+\frac{y}{4}\right) = \frac{x^2}{9} - \frac{y^2}{16}\)

22, \(\left(\frac{x}{y}-\frac{2}{3}\right)\left(\frac{x}{y}+\frac{2}{3}\right) = \frac{x^2}{y^2} - \frac{4}{9}\)

23, \(\left(\frac{y}{2}+\frac{x}{3}\right)\left(\frac{y}{2}-\frac{x}{3}\right) = \frac{y^2}{4} - \frac{x^2}{9}\)

24, \(\left(2x-\frac{2}{3}\right)\left(\frac{2}{3}+2x\right) = 4x^2 - \frac{4}{9}\)

25, \(\left(2x+\frac{3}{5}\right)\left(\frac{3}{5}-2x\right) = \frac{9}{25} - 4x^2\)

26, \(\left(\frac{1}{2}x-\frac{4}{3}\right)\left(\frac{4}{3}+\frac{1}{2}x\right) = \frac{1}{4}x^2 - \frac{16}{9}\)

27, \(\left(\frac{2}{3}x^2-\frac{y}{2}\right)\left(\frac{2}{3}x^2+\frac{y}{2}\right) = \frac{4}{9}x^4 - \frac{y^2}{4}\)

28, \((3x-y^2)(3x+y^2) = 9x^2 - y^4\)

29, \((x^2-2y)(x^2+2y) = x^4 - 4y^2\)

30, \((x^2-y^2)(x^2+y^2) = x^4 - y^4\)

`x^2 -2x = 24`

` x^2 -2x - 24 = 0`

`x^2 + 4x - 6x - 24 = 0 `

`x(x+4) - 6(x+4)= 0 `

`(x+4) (x-6) = 0`

TH`1`
`x+4 = 0 => x=-4 `
TH`2`
`x-6 = 0 => x=6 `
Vậy....

x^2-2x=24

x^2-2x-24

△=b^2-4ac=(-2)^2-4*1*(-24)=100

⇒△>0 hay pt trên có hai nghiệm phân biệt x1,x2

x1=(-b+√△)/2a=(-(-2)+√100 )/2*1=6

x2=(-b-√△)/2a=(-(-2)-√100 )/2*1=-4

vậy x1=6 ; x2=-4

mình đánh máy bạn thông cảm =))

\(x^2-2x=24\)

\(\Rightarrow x^2-2x+1=24+1\)

\(\Rightarrow\left(x-1\right)^2=25\)

\(\Rightarrow\left(x-1\right)^2=5^2\)

\(\Rightarrow\left[\begin{array}{l}x-1=5\\ x-1=-5\end{array}\right.\)

\(\Rightarrow\left[\begin{array}{l}x=6\\ x=-4\end{array}\right.\)

Vậy \(x\in\left\lbrace6;-4\right\rbrace\)