Question

Phân tích đa thức sau thành nhân tử

a) \(a^4b^4+a^3b-abc\)

b) \(-x^2y^2z^2-6x^3y-8x^4z^2-9x^5y^5z^5\)

c) \(16x^2-9\left(x+y\right)^2\)

d) \(\left(a-b\right)^2-1\)

e) \(a^6-b^6\)

Answer 1

a) \(a^4b^4+a^3b-abc=ab\left(a^3b^3+a^2-c\right)\)

b) \(-x^2y^2z^2-6x^3y-8x^4z^2-9x^5y^5z^5\)

\(=x^2\left(-y^2z^2-6xy-8x^2z^2-9x^3y^5z^5\right)\)

c) \(16x^2-9\left(x+y\right)^2=\left(4x\right)^2-\left(3x+3y\right)^2=\left(7x+3y\right)\left(x-3y\right)\)

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

e) \(a^6-b^6\)

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

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