Factor completely.50q2–128

Sure, let's factor the expression 50q^2 - 128 completely.

Step 1: Identify the greatest common factor (GCF) The GCF of 50 and 128 is 2. So, we can factor out 2 from the expression.

2(25q^2 - 64)

Step 2: Recognize the difference of squares The expression inside the parentheses is a difference of squares. It can be factored as follows:

a^2 - b^2 = (a - b)(a + b)

Here, a = 5q and b = 8. So, we can factor the expression as follows:

2(5q - 8)(5q + 8)

So, the expression 50q^2 - 128 is completely factored as 2(5q - 8)(5q + 8).