Question

Phân tích đa thức sau thành nhân tử:

h) \(a^2-2a^2b+ab^2\)

i) \(5ax^4+10ax^3y+5ax^2y^2\)

j) \(2x^2+4x+2-2y^2\)

k1) \(2xy-x^2-y^2+9\)

k2) \(x^3+2x^2y+xy^2-16x\)

l)\(a^3-a^2-a+1\)

Answer 1

h: \(a^2-2a^2b+ab^2\)

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

i: \(5ax^4+10ax^3y+5ax^2y^2\)

\(=5ax^2\left(x^2+2xy+y^2\right)\)

\(=5ax^2\left(x+y\right)^2\)

j: \(2x^2+4x+2-2y^2\)

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

\(=2\left(x+1+y\right)\left(x+1-y\right)\)

k1: \(2xy-x^2-y^2+9\)

\(=9-\left(x^2-2xy+y^2\right)\)

\(=9-\left(x-y\right)^2\)

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

k2: \(x^3+2x^2y+xy^2-16x\)

\(=x\left(x^2+2xy+y^2-16\right)\)

\(=x\left(x+y+4\right)\left(x+y-4\right)\)

l: \(=a^2\left(a-1\right)-\left(a-1\right)\)

\(=\left(a-1\right)\left(a^2-1\right)\)

\(=\left(a-1\right)^2\cdot\left(a+1\right)\)