Question

X^4+4y^4 phân tích đa thức thành nhân tử

Answer 1

x⁴ + 4y⁴ 

= (x²)² + 4x²y² + (2y²)² - 4x²y²

= (x² + 2y²)² - (2xy)²

= (x² + 2y² - 2xy)(x² + 2y² + 2xy)

Answer 2

\(x^4+4y^4\)

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

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

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

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

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