Question

b1: phân tích các số sau thành nhân tử 
a)x^8+x^4+1
b)(x^2+1)^2+3x(x^2+1)+2x^2

Answer 1

a: \(x^8+x^4+1\)

\(=x^8+2x^4+1-x^4\)

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

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

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

\(=\left(x^4-x^2+1\right)\cdot\left[\left(x^2+1\right)^2-x^2\right]\)

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

b: \(\left(x^2+1\right)^2+3x\left(x^2+1\right)+2x^2\)

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

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

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

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