Question

Phân tích thành nhân tử:
a) x⁴y⁴ +4
b) 32x⁴ +1

c) x⁴ +4y⁴

d) x⁷ +x² +1
e) x¹⁰ +x⁵ +1

Answer 1

e: \(x^{10}+x^5+1\)

\(=x^{10}-x+\left(x^5-x^2\right)+x^2+x+1\)

\(=x\left(x^9-1\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+x^2+x+1\)

\(=x\left(x^3-1\right)\left(x^6+x^3+1\right)+\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)

\(=\left(x^2+x+1\right)\left[x\left(x-1\right)\left(x^6+x^3+1\right)+x^3-x^2+1\right]\)

c: \(x^4+4y^4\)

\(=x^4+4x^2y^2+4y^4-4x^2y^2\)

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

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