Factorize 625a² -81b⁸

Answer 1

To factorize the expression 625a² - 81b⁸, we need to recognize that this is a difference of two squares.

First, rewrite the expression as follows:

625a² - 81b⁸ = (25a)² - (9b⁴)²

Now, we can apply the formula for the difference of squares:

(a² - b²) = (a + b)(a - b)

In this case, a = 25a and b = 9b⁴. Thus, the factorization is:

625a² - 81b⁸ = (25a + 9b⁴)(25a - 9b⁴)

Therefore, 625a² - 81b⁸ factors as (25a + 9b⁴)(25a - 9b⁴).