I need help factoring 64b^2-(q+r)^2

difference of two squares (a^2-b^2 =(a-b)(a+b) in general

here (8b-(q+r))(8b+(q+r))
= (8b-q-r)(8b+q+r)

To factor the expression 64b^2-(q+r)^2, let's start by recognizing that it is a difference of squares.

The difference of squares formula is:
a^2 - b^2 = (a + b)(a - b)

In this case, a represents 8b and b represents (q+r). So we can rewrite the expression as:

(8b)^2 - (q+r)^2

Now we can apply the difference of squares formula:

(8b + (q+r))(8b - (q+r))

Therefore, the factored form of 64b^2 - (q+r)^2 is:
(8b + q + r)(8b - q - r)

And that's how you factor the given expression.