Question

Phân tích các đa thức sau thành nhân tử:

a) (a+b+c)(ab+bc+ca)-abc

b) xyz-(xy+yz+zx)+(x+y+z)-1

c) ab(a+b)+bc(b-c)-ca(c+a)

d) x(x+2y)³-y(y+2x)³

Answer 1

a: \(=\left(a+b\right)\left(ab+bc+ca\right)+c\left(ab+bc+ca\right)-abc\)

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

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

=(a+b)(b+c)(a+c)

d: \(=x\left(x^3+6x^2y+12xy^2+8y^3\right)-y\left(8x^3+12x^2y+6xy^2+y^3\right)\)

\(=x^4+6x^3y+12x^2y^2+8xy^3-8x^3y-12x^2y^2-6xy^3-y^4\)

\(=x^4-y^4-2x^3y+2xy^3\)

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

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