Question

Toán vận dụng: phân tích đa thức: x⁴-y⁴+2x³y-2xy³ thành nhân tử (x+y).(x²-y²)

Answer 1

\(x^4-y^4+2x^3y-2xy^3\)

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

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

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

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

Answer 2

\(x^4-y^4+2x^3y-2xy^3\\ =\left(x^2\right)^2-\left(y^2\right)^2+2xy\left(x^2-y^2\right)\\ =\left(x^2-y^2\right)\left(x^2+y^2\right)+2xy\left(x^2-y^2\right)\\ =\left(x^2-y^2\right)\left(x^2+y^2+2xy\right)\\ =\left(x-y\right)\left(x+y\right)\left(x+y\right)^2\\ =\left(x-y\right)\left(x+y\right)^3\)