Question

Phân tích các đa thức sau thành nhân tử

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

b) \(x^4+x^3+x+x+1\)

c) \(a^3x-ab+b-x\)

d) \(a^2-b^2-a+b\)

Answer 1

a) (x+1)² - (x-1)²

= (x² + 2.x.1 + 1²) - (x²-2.x.1+1²)

= x²+2x+1 - x²+2x-1

= (x²-x²) + (2x+2x) + (1-1)

=4x

Answer 2

c: \(=x\left(a^3-1\right)-b\left(a-1\right)\)

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

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

d: \(=\left(a-b\right)\left(a+b\right)-\left(a-b\right)=\left(a-b\right)\left(a+b-1\right)\)

a: \(=\left(x+1+x-1\right)\left(x+1-x+1\right)=2\cdot2x=4x\)