`a)(x+2)^2+2(x^2-4)+(x-2)^2`

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

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

`b)x^2-x+1/4`

`=x^2-2.x .1/2+1/4=(x-1/2)^2`

`c)(x+y)^3-(x-y)^3`

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

`=2y(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)`

`=2y(3x^2+y^2)`

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

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

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

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

c) \(\left(x+y\right)^3-\left(x-y\right)^3=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x^3-3x^2y+3xy^2-y^3\right)=6x^2y+2y^3=2y\left(3x^2+y^2\right)\)

\(a,2x-2\sqrt{x}=2\sqrt{x}\left(\sqrt{x}-1\right)\\ b,x-\sqrt{x}-6=x-3\sqrt{x}+2\sqrt{x}-6\\ =\sqrt{x}\left(\sqrt{x}-3\right)+2\left(\sqrt{x}-3\right)=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\\ c,4x-4\sqrt{x}+1=\left(2\sqrt{x}\right)^2-2.2\sqrt{x}.1+1^2=\left(2\sqrt{x}+1\right)^2\)

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

b) \(x-\sqrt{x}-6=\left(\sqrt{x}-3\right)\left(\sqrt{x}+2\right)\)

c) \(4x-4\sqrt{x}+1=\left(2\sqrt{x}-1\right)^2\)

a) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\left(1\right)=\left[\left(x+1\right)\left(x+4\right)\right]\left[\left(x+2\right)\left(x+3\right)\right]-15=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)

Đặt \(t=x^2+5x+4\)

(1) trở thành: \(t\left(t+2\right)-15=t^2+2t+1-16=\left(t+1\right)^2-4^2=\left(t-3\right)\left(t+5\right)\)

Thay t: \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-15=\left(x^2+5x+4-3\right)\left(x^2+5x+4+5\right)=\left(x^2+5x+1\right)\left(x^2+5x+9\right)\)

b) \(\left(2x+5\right)^2-\left(x-9\right)^2=\left(2x+5-x+9\right)\left(2x+5+x-9\right)=\left(x+14\right)\left(3x-4\right)\)

a: Ta có: \(\left(x+1\right)\cdot\left(x+2\right)\left(x+3\right)\left(x+4\right)-15\)

\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-15\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24-15\)

\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+9\)

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

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

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

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

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

b) \(4x^2 -8x+3 \\= (2x^2)-2.2x .2 + 2^2 -1 \\=(2x-2)^2-1^2\\=(2x-2+1)(2x-2-1)\\= (2x-1)(2x-3)\)

a: \(x\left(x^3-4\right)+2x^3-4\)

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

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

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

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

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

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

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

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

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

Bn ấn vào câu hỏi của bn sẽ rs những câu tương tự có đáp án nhé!!Chúc bn lm đc bài này nha!!

Trả lời:

A=(x-1)(x+2)(x-3)(x+4)-144

A= (x²-5x-14)(x²-5x-24)-144 (1)

đặt m=x²-5x-14

=> A= m.(m-10)-144

A=m²-10m-144

A= (m-18)(m+8)

thay m vào, ta có:

A= (x²-5x-32)(x²-5x-6)

A=(x²-5x-32)(x+1)(x-6)

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

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

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

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

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

\(=\left(x+1\right)\left[\left(x+1\right)-3\right]\)

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

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

c) \(2x\left(x-2\right)-\left(x-2\right)^2\)

\(=\left(x-2\right)\left[2x-\left(x-2\right)\right]\)

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

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

a: \(=5a\left(x-2y\right)\)

b: \(=x\left(x-y\right)+\left(x-y\right)=\left(x-y\right)\left(x+1\right)\)

c: =(x-1)(x-7)

a)\(5ax-10ay=5a\left(x-2y\right)\)

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

c) \(x^2-8x+7=\left(x-7\right)\left(x-1\right)\)

a)5a(x-2y)

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

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

\(\left(x+1\right)\left(x-y\right)\)

c)\(x^2-x-7x+7\)

\(x\left(x-1\right)-7\left(x-1\right)\)

\(\left(x-1\right)\left(x-7\right)\)

\(a,x^2-ax+5x-5a=x\left(x-a\right)+5\left(x-a\right)=\left(x-a\right)\left(x+5\right)\\ b,x^3-4x^2+4x=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\\ c,x^2-2x-y^2+1=\left(x^2-2x+1\right)-y^2=\left(x-1\right)^2-y^2=\left(x-y-1\right)\left(x+y-1\right)\)

a) (x²-6x+9)-y²=(x-3)²-y²=(x-3-y)(x-3+y)