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

áp dụng a+b+c =0 => a3 +b3+c3=3abc

Answer 2

b: \(=\left(b-c+c-a\right)^3-3\left(b-c\right)\left(c-a\right)\left(b-c+c-a\right)-\left(b-a\right)^3\)

\(=-3\left(b-c\right)\left(c-a\right)\left(b-a\right)\)

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

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