Question

Factor (3c + 2)^2 - (3c - 2)^2

Answer 1

Hi there! Your answe is 24c

Please see an explanation below for a clear understanding to your problem.

Any questions about my explanation and answer can be asked through comments! :)

Step-by-step explanation:

$\large \boxed{ {x}^{2} - {y}^{2} = (x + y)( x - y)}$

The formula above is what we will be using. This is called "Difference of Two Squares".

Notice how the these expressions are similar to the formula's structure.

$\large{ {(3c + 2)}^{2} - {(3c - 2)}^{2} }$

Notice how there are minus sign, squared expression which we can factor by using the formula above. Therefore -

$\large{ {x}^{2} = {(3c + 2)}^{2} } \\ \large{x = 3c + 2}$

Therefore, our y would be 3c-2.

Then proceed with the formula.

$\large{ {(3c + 2)}^{2} - {(3c - 2)}^{2} = (3c + 2 + 3c - 2)(3c + 2 - (3c - 2))}$

Simplify.

$\large{ (6c)(3c + 2 - 3c + 2)} \\ 6c(4) \\ 24c$