Question

m) \(m^2+am+ay-y^2\)

n) \(3xy+y^2-3x-1\)

o) \(x^3-xy^2+x^2y-y^3\)

p) \(a^3-ma-mb+b^3\)

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

s) \(xy\left(x+y\right)+yz\left(y+z\right)+xz\left(x+z\right)+2xyz\)

Phân tích đa thức thành nhân tử

Answer 1

o: \(x^3-xy^2+x^2y-y^3\)

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

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

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

p: \(a^3-ma-mb+b^3\)

\(=\left(a+b\right)\left(a^2-ab+b^2\right)-m\left(a+b\right)\)

\(=\left(a+b\right)\left(a^2-ab+b^2-m\right)\)

q: \(\left(3x+1\right)^3-\left(1-2x\right)^3\)

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

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

\(=5x\left[9x^2+6x+1-6x^2+3x-2x+1+4x^2-4x+1\right]\)

\(=5x\left(7x^2+5x+3\right)\)