Question

Phân tích thành nhân tử:

a) 4x² - y² +4x + 1;

b) x³ - x + y³ - y.

Answer 1

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

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

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

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

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

Answer 2

a) 4x²-y²+4x+1=(4x²+4x+1)-y²=(2x+1)²-y² = (2x+1-y)(2x+1+y)

b) x³-x+y³-y=(x³+y³)-(x+y)=(x+y)(x²-xy+y²)-(x+y) = (x+y)(x²-xy+y²-1)