Câu hỏi của Đỗ thị như quỳnh

Question

Phân tích thành nhân tử :

a, $x^2-2x-4y^2-4y$

b, $x^2\cdot\left(1-x^2\right)-4-4x^2$

c, $x^3+2x^2+2x+1$

d, $x^4-2x^3+2x-1$

Yukru · Accepted Answer

a) $x^2-2x-4y^2-4y$

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

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

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

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

b) Mình nghĩ câu này sai đề

c) $x^3+2x^2+2x+1$

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

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

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

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

d) $x^4-2x^3+2x-1$

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

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

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

$=\left(x+1\right)\left(x-1\right)^3$Câu trả lời: a) $x^2-2x-4y^2-4y$