Question

Phân tích đa thức thành nhân tử

\(x^3+3x^2y-9xy^2+5y^2\)

\(x^8y^8+x^4y^4+1\)

Answer 1

\(x^8y^8+x^4y^4+1=\left[\left(x^4y^4\right)^2+2x^4y^4+1\right]-x^4y^4=\left(x^4y^4+1\right)^2-\left(x^2y^2\right)^2\)

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

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

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

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

Answer 2

Phân tích đa thức thành nhân tử

x³+3x²y−9xy²+5y²

x⁸y⁸+x⁴y⁴+1