Question

phân tích đa thức thành nhân tử:

a. x⁴ + x³y - xy³ - y⁴

b. a⁴ + 3a²b² + 4b²

c. 9a³ - 13a + 6

Answer 1

\(x^4+x^3y-xy^3-y^4=\left(x^4-y^4\right)+\left(x^3y-xy^3\right)\)

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

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

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

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

Answer 2

b: \(=a^4+4a^2b^2+4b^2-a^2b^2\)

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

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

c:

Sửa đề: \(9a^3-13a+6\) 

\(=9a^3-6a^2+6a^2-4a-9a+6\)

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