a^2 - 4a + 4 - 64b^2

Question

Factor completely

Answer 1

Hello Delilah,

 

Thank you for posting the question. Here is my approach. I am providing you with a similar example. This can be solved by re-grouping the terms:

 

Ex.: x²-16x+16-49y²

 

If you remember your 3 basic factorization types:

1. (a+b)(a+b) = (a+b)²=a²+2ab+b²

2. (a-b)(a-b) = (a-b)² =a²-2ab+b²

3. (a+b)(a-b) = a²-b²

 

In this example, you can re-group the perfect squares first:

x²-49y² => this follows the 3rd type and will be factored as:

(x+7y)(x-7y) = x²-7xy+7xy-49y² = x²-49y²

 

Next, you take the remaining factors from the above problem:

-16x+16 => -16(x-1)

 

and re-write the completely factored answer:

(x+7y)(x-7y) - 16 (x-1)

================

 

I hope this helps solve your original problem. Good luck!