Question

phân tích đa thức thành nhân tử

a/x^2(x+1)^2-4(x^2+x+1)^2

b/x^2+y^2+3x-3y-2xy+10

c/a^2-27-(3-a)(6a+9)

d/6(x^2+x)^2+x^2+x-1

Answer 1

a: \(x^2\left(x+1\right)^2-4\left(x^2+x+1\right)^2\)

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

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

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

b: Sửa đề: \(x^2+y^2-2xy+3x-3y-10\)

\(=\left(x-y\right)^2+3\left(x-y\right)-10\)

\(=\left(x-y+5\right)\left(x-y-2\right)\)

c: \(a^3-27-\left(3-a\right)\left(6a+9\right)\)

\(=\left(a-3\right)\left(a^2+3a+9\right)+\left(a-3\right)\left(6a+9\right)\)

\(=\left(a-3\right)\left(a^2+9a+18\right)\)

\(=\left(a-3\right)\left(a+3\right)\left(a+6\right)\)