Bài 8: Phân tích đa thức thành nhân tử bằng phương pháp nhóm các hạng tử

\(9-x^2+2xy-y^2\)

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

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

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

\(=\left[3-\left(x-y\right)\right]\left[3+\left(x-y\right)\right]\)

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

\(49\left(y-4\right)^2-9\left(y+2\right)^2\)

\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)

\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)

\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)

\(=\left(4y-34\right)\left(10y-22\right)\)

\(=4\left(2y-17\right)\left(5y-11\right)\)

\(16-9^2\\=4^2-9^2\\=(4-9)(4+9)\\=-5\cdot13\\=-65\)

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

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

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

\(2x^2-7\sqrt{x}+5\)

\(=2x^2+2x\sqrt{x}+2x-5\sqrt{x}-2x\sqrt{x}-2x-2\sqrt{x}+5\)

\(=\left(2x^2+2x\sqrt{x}+2x-5\sqrt{x}\right)-\left(2x\sqrt{x}+2x+2\sqrt{x}-5\right)\)

\(=\sqrt{x}\left(2\sqrt{x}+2x+\sqrt{x}-5\right)-\left(2x\sqrt{x}+2x+2\sqrt{x}-5\right)\)

\(=\left(\sqrt{x}-1\right)\left(2x\sqrt{x}+2x+2\sqrt{x}-5\right)\)

Không phân tích được bạn nhé. Bạn coi lại đề.

1) \(x^2-25\)

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

\(=\left(x-5\right)\left(x+5\right)\)

2) \(9x^2-\dfrac{1}{16}y^2\)

\(=\left(3x\right)^2-\left(\dfrac{1}{4}y\right)^2\)

\(=\left(3x-\dfrac{1}{4}y\right)\left(3x+\dfrac{1}{4}y\right)\)

3) \(x^6-y^4\)

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

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

4) \(\left(2x-5\right)^2-64\)

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

\(=\left(2x-5-8\right)\left(2x-5+8\right)\)

\(=\left(2x-13\right)\left(2x+3\right)\)

5) \(81-\left(3x+2\right)^2\)

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

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

\(=\left(7-3x\right)\left(3x+11\right)\)

6) \(9\left(x-5y\right)^2-16\left(x+y\right)^2\)

\(=\left[3\left(x-5y\right)\right]^2-\left[4\left(x+y\right)\right]^2\)

\(=\left(3x-15y-4x-4y\right)\left(3x-15y+4x+4y\right)\)

\(=\left(-x-19y\right)\left(8x-11y\right)\)

7: x^3-8

=x^3-2^3

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

8: 27x^3+125y^3

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

=(3x+5y)(9x^2-15xy+25y^2)

9: x^6+216

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

=(x^2+6)(x^4-6x^2+36)

10: x^2+8x+16=(x+4)^2

11: 9x^2-12xy+4y^2=(3x-2y)^2

12: =-(25x^2y^2-10xy+1)=-(5xy-1)^2

13: =x^3-3*x^2*2+3*x*2^2-2^3

=(x-2)^3

14: =(2x)^3+3*(2x)^2*y+3*2x*y^2+y^3

=(2x+y)^3

15: \(=2xy\left(x^2+y^2+2xy-1\right)\)

\(=2xy\left[\left(x+y\right)^2-1\right]\)

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

16: =(x-y)^2+4(x-y)

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

17: =x^3+3x^2y+3xy^2+y^3-x-y

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

=(x+y)[(x+y)^2-1]

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

18: =(x-y)^2-4z^2

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

19: =x^2-y^2-(x+y)

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

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

20: =(x-y)^2-z^2

=(x-y-z)(x-y+z)

1:

=3x^2+9x-2x-6

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

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

2: =3(x^2+x-2)

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

=3[x(x+2)-(x+2)]

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

3: =3(x^2-x-2)

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

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

4: =6x^2-9x-4x+6

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

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

5: =6x^2+9x+4x+6

=3x(2x+3)+2(2x+3)

=(2x+3)(3x+2)

6: =3(2x^2+5x+2)

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

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

7: =3(2x^2-5x+2)

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

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

8: =2(3x^2+10x+3)

=2(3x^2+9x+x+3)

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