Question

find the factors a⁴-b⁴​

Answer 1

The given expression is

a⁴-b⁴​

Write this expression in perfect square form

(a²)²-(b²)²

Use the formula for difference of squares: x²-y²=(x+y)(x-y)

(a²+b²)(a²-b²)

Again apply the formula for difference of squares

(a²+b²)(a+b)(a-b)

Thus, the factor of a⁴-b⁴​ is (a²+b²)(a+b)(a-b).

Answer 2

Given:

The given expression is  a⁴-b⁴​

Find:

find the factors of the given expression.

Let,

Write this expression in perfect square form

(a²)²-(b²)²

Now,

Use the formula for the difference of squares:

x²-y²=(x+y)(x-y)

(a²+b²)(a²-b²)

Again apply

The formula for the difference of squares

(a²+b²)(a+b)(a-b)

Thus, the factor of a⁴-b⁴​ is (a²+b²)(a+b)(a-b).