Question

Phân tích đa thức thành nhân tử :

\(4x^4+4x^2y^2-8y^4\)

Answer 1

\(4x^4+4x^2y^2-8y^4\)

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

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

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

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

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

Answer 2

4x⁴ + 4x²y² - 8y⁴ = 4x⁴ + 8x²y² - 4x²y² - 8y⁴

= 4x²(x² + 2y²) - 4y²(x² - 2y²)

= (x² - 2y²)(4x² - 4y²)

= 4(x² - 2y²)(x² - y²)

= 4(x² - 2y²)(x - y)(x + y)