Question

Phân tích thành nhân tử:

(1 + 2x)(1-2x) - x(x + 2)(x - 2)

Answer 1

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

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

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

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

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

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

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

Chúc bạn học tốt!!!

Answer 2

Ta có : $(1+2x)(1-2x)-x(x+2)(x-2)$

$=1-4x^2-x(x^2-4)$

$=1-4x^2-x^3+4x$

$=-x^3-4x^2+4x+1$

$=(-x^3+x^2)-(5x^2-5x)-(x-1)$

$=(x-1).(-x^2)-5x(x-1)-(x-1)$

$=(x-1)(-x^2-5x-1)$