Question

Phân tích đa thức sau thành nhân tử :

\(i,\left(b-c\right)^3+\left(c-a\right)^3+\left(a-b^3\right)\)

\(k,\left(x^2+y^2\right)^3+\left(z^2-x^2\right)^3-\left(y^2+z^2\right)^3\)

Answer 1

i: \(=\left(b-c+c-a\right)\left[\left(b-c\right)^2-\left(b-c\right)\left(c-a\right)+\left(c-a\right)^2\right]+\left(a-b\right)^3\)

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

\(=\left(b-a\right)\left(b^2+3c^2+a^2-3bc+ab-3ac\right)+\left(a-b\right)\)

\(=\left(b-a\right)\left(b^2+3c^2+a^2-3bc+ab-3ac-1\right)\)

k: \(=\left(x^2+y^2+z^2-x^2\right)^3-3\left(x^2+y^2\right)\left(z^2-x^2\right)\left(y^2+z^2\right)-\left(y^2+z^2\right)^3\)

\(=-3\left(x^2+y^2\right)\left(z-x\right)\left(z-x\right)\left(y^2+z^2\right)\)