Question

x^4 - y^4 divided by x+y​

Answer 1

Answer:

(x⁴ - y⁴)/(x+y)

[(x²)² - (y²)²]/(x+y)

[(x²+y²)(x²-y²)]/(x+y)

(x²+y²)(x+y)(x-y)/(x+y)

(x²+y²)(x-y)

Answer 2

Answer:

(x² + y²)(x - y)

Step-by-step explanation:

Given : (x⁴ - y⁴) / (x + y)

First, we solve (x⁴ - y⁴)

→ x⁴ - y⁴

We can also write this as :

→ (x²)² - (y²)²

Identity : a² - b² = (a + b)(a - b)

Here, a = x², b = y²

→ (x² + y²)(x² - y²)

This can also be written as :

→ (x² + y²)[(x)² - (y)²]

Again using the above identity.

Here, a = x, b = y

→ (x² + y²)[(x + y)(x - y)]

→ (x² + y²)(x + y)(x - y)

Returning to the question, we get

→ [ (x² + y²)(x + y)(x - y) ] / (x + y)

→ (x² + y²)(x - y)