Question

Answer 1

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

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

\(x^2+6x+9=\left(x+3\right)^2\)

\(x^2+10x+25=\left(x+5\right)^2\)

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

\(9x^2-6x+1=\left(3x-1\right)^2\)

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

\(4x^2-12x+9=\left(2x-3\right)^2\)

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

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

Answer 2

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

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

\(9x^2-16y^2=\left(3x-4y\right)\left(3x+4y\right)\)

\(\dfrac{1}{4}x^2-9y^2=\left(\dfrac{1}{2}x\right)^2-\left(3y\right)^2=\left(\dfrac{1}{2}x-3y\right)\left(\dfrac{1}{2}x+3y\right)\)

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

\(\left(3x+5\right)^2-4=\left(3x+5\right)^2-2^2=\left(3x+5-2\right)\left(3x+5+2\right)=\left(3x+3\right)\left(3x+7\right)\)

\(\left(2x+3\right)^2-16x^2=\left(2x+3\right)^2-\left(4x\right)^2=\left(2x+3-4x\right)\left(2x+3+4x\right)=\left(3-x\right)\left(6x+3\right)\)

Answer 3

\(4\left(3x+1\right)^2-9=\left(6x+2\right)^2-3^2=\left(6x+2-3\right)\left(6x+2+3\right)=\left(6x-1\right)\left(6x+5\right)\)

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

\(=-5\left(x+5\right)\left(x+1\right)\)

\(\left(3x-2\right)^2-16=\left(3x-2\right)^2-4^2=\left(3x-2-4\right)\left(3x-2+4\right)=\left(3x-6\right)\left(3x+2\right)=3\left(x-2\right)\left(3x+2\right)\)

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

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

Answer 4

\(\left(3x+1\right)^2-\left(x+3\right)^2=\left(3x+1-x-3\right)\left(3x+1+x+3\right)=\left(2x+2\right)\left(4x+4\right)=8\left(x+1\right)^2\)

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

\(8x^3-27=\left(2x\right)^3-3^3=\left(2x-3\right)\left(4x^2+6x+9\right)\)

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

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

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

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

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

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

Answer 5

giúp e hết bài vs ạ

Answer 6

giúp e từ câu 1=>29 vs

Answer 7

bạn ơi bạn chia nhỏ câu ra đi dài quá

Answer 8

27) \(\left(x^2+9\right)^2-36x^2=\left(x^2-6x+9\right)\left(x^2+6x+9\right)=\left(x-3\right)^2\cdot\left(x+3\right)^2\)

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

26) \(8x^3-27=\left(2x-3\right)\left(4x^2+6x+9\right)\)

Answer 9

1) \(x^2-2x+1=\left(x-1\right)^2\)

2) \(x^2-4x+4=\left(x-2\right)^2\)

3) \(x^2+6x+9=\left(x+3\right)^2\)

4) \(x^2+10x+25=\left(x+5\right)^2\)

Answer 10

5) \(4x^2-4x+1=\left(2x-1\right)^2\)

6) \(9x^2-6x+1=\left(3x-1\right)^2\)

7) \(9x^2+12x+4=\left(3x+2\right)^2\)

8) \(4x^2-12x+9=\left(2x-3\right)^2\)

Answer 11

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

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

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

12) \(4x^2-9=\left(2x-3\right)\left(2x+3\right)\)

Answer 12

13) \(9x^2-16y^2=\left(3x-4y\right)\left(3x+4y\right)\)

14) \(\dfrac{1}{4}x^2-9y^2=\left(\dfrac{1}{2}x-3y\right)\left(\dfrac{1}{2}x+3y\right)\)

15) \(\dfrac{9}{4}x^2-25y^2=\left(\dfrac{3}{2}x-5y\right)\left(\dfrac{3}{2}x+5y\right)\)

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

Answer 13

17) \(\left(3x+5\right)^2-4=\left(3x+5-2\right)\left(3x+5+2\right)=3\left(x+1\right)\left(3x+7\right)\)

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

19) \(4\left(3x+1\right)^2-9=\left(6x+2\right)^2-3^2=\left(6x-1\right)\left(6x+5\right)\)

20) \(\left(2x-5\right)^2-9x^2=\left(2x-5-3x\right)\left(2x-5+3x\right)=5\left(x-1\right)\left(-x-5\right)\)

Answer 14

21) \(\left(3x-2\right)^2-16=\left(3x-2-4\right)\left(3x-2+4\right)=3\left(x-2\right)\left(3x+2\right)\)

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

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

24) \(\left(3x+1\right)^2-\left(x+3\right)^2=\left(3x+1-x-3\right)\left(3x+1+x+3\right)=8\left(x+1\right)\left(x-1\right)\)

 

Answer 15

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

26) \(8x^3-27=\left(2x-3\right)\left(4x^2+6x+9\right)\)

27) \(\left(x^2+9\right)^2-36x^2=\left(x^2-6x+9\right)\left(x^2+6x+9\right)=\left(x-3\right)^2\cdot\left(x+3\right)^2\)

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

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

 

Answer 16

29) \(4x^2-\left(x^2+1\right)^2=\left(2x-x^2-1\right)\left(2x+x^2+1\right)=-\left(x-1\right)^2\cdot\left(x+1\right)^2\)