Câu hỏi của Pham Ngoc Linh

Question

Phan tich cac da thuc sau thanh nhan tu:

a, -4x2+4x-1

b,(2x+1)2-4(x-1)2

c,(2x+y)2-4x2+12x-9

d, (x+1)2-4(x+1)y2+4y4

B.Thị Anh Thơ · Accepted Answer

a,$-4x^2+4x-1$

$\Leftrightarrow\left(-2x-1\right)^2$

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

$\Rightarrow\left[2x+1-2\left(x-1\right)\right].\left[2x+1+2\left(x-1\right)\right]$

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

$\Rightarrow3\left(4x-1\right)$

c,$\left(2x-y\right)^2-4x^2+12x-9$

$\Leftrightarrow\left(2x+y\right)^2-\left(4x^2-12x+9\right)$

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

$\Leftrightarrow\left(2x+y-2x+3\right)\left(2x+y+2x-3\right)$

$\Rightarrow\left(y+3\right)\left(4x+y-3\right)$

d,$\left(x+1\right)^2-4\left(x+1\right)y^2+4y^4$

$\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+2^2y^4$

$\Leftrightarrow\left(x+1\right)^2-2\left(x+1\right)2y^2+4\left(y^2\right)^2$

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

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