Question

Phân tích đa thức thành nhân tử:

a) \(a\left(a-b\right)^2\left(a+b\right)-\left(b-a\right)^2\left(a^2-5ab+b^2\right)\)

b) \(x^6-y^6\)

c) \(x^3+2x^2-3x+6\)

d) \(x^5-x^4y-xy^4+y^5\)

Answer 1

c) Sửa đề: \(x^3+2x^2-3x-6\)

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

d) \(x^5-x^4y-xy^4+y^5=x^4\left(x-y\right)-y^4\left(x-y\right)\)

\(=\left(x-y\right)\left(x^4-y^4\right)=\left(x-y\right)\left(x^2-y^2\right)\left(x^2+y^2\right)\)

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

True?

Answer 2

a) \(=a\left(a-b\right)^2\left(a+b\right)-\left(a-b\right)^2\left(a^2-5ab+b^2\right)\)

\(=\left(a-b\right)^2\left(a^2+ab-a^2+5ab-b^2\right)=\left(a-b\right)^2\left(6ab-b^2\right)\)

\(=b\left(a-b\right)^2\left(6a-b\right)\)

b) \(x^6-y^6=\left(x^3-y^3\right)\left(x^3+y^3\right)\)

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