Question

factorise x^4-y^4 using identities​

Answer 1

Answer :

›»› x⁴ - y⁴ = (x - y) (x + y) (x² + y²)

Given :

• x⁴ - y⁴

To Find :

• Factorize the expression.

Required Solution :

Let's start solving the problem and understand the steps to get our final result$.$

⇛ x⁴ - y⁴

Present the shape of the power,

⇛ (x²)² - y⁴

Present the shape of the power,

⇛ (x²)² - (y²)²

Organize by using A² - B² = (A - B) (A - B),

⇛ (x² + y²) (x² - y²)

Factorize to use the polynomial formula of sum and difference,

⇛ (x² + y²) (x + y) (x - y)

Sort the factor,

⇛ (x - y) (x + y) (x² + y²)

║Hence, the factorization of x⁴ - y⁴ is (x - y) (x + y) (x² + y²).║