Question

phân tích đa thức thành nhân tử x²(x+1)-2x(x+1)+x+1

a²+b²+2a-2b-2ab

Answer 1

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

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

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

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

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

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

\(=\left(a^2-2ab+b^2\right)+\left(2a-2b\right)\)

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

\(=\left(a-b\right)\left(a-b+2\right)\)

Answer 2

a) x²( x + 1)- 2x( x + 1)+ x + 1

= ( x + 1)( x² - 2x + 1)

= ( x + 1)( x - 1)²

b) a²+ b²+ 2a - 2b- 2ab

= ( a - b)² + 2( a - b)

= ( a - b)( a - b + 2)