Question

Factor the following expression, and verify that the factored expression is equivalent to the original: 4x^2-9a^6

Answer 1

(2x - 3a³) ,(2x + 3a³)

Explanation:

Given that

4x^2-9a^6

As we know that

x² - y² = ( x+y)(x-y)

So

4x^2-9a^6 = (2x)² - (3a³)²

By using the above formula

x² - y² = ( x+y)(x-y)

4x^2-9a^6 = (2x)² - (3a³)²

4x^2-9a^6 = (2x - 3a³) (2x + 3a³)

So the factor is (2x - 3a³) ,(2x + 3a³)

To verify

Multiple both factors

(2x - 3a³) (2x + 3a³) = 2x .2x -2x . 3a³ + 3a³ . 2x - 3a³. 3a³

=4x² - 9 a ⁶