How do you factor 4x squared -49?

Answer 1

53

Answer 2

This binomial is an example of what is called a "difference of squares". This type of binomial is of the form:

a2-b2

This type of binomial can be factored to:

a2-b2 = (a+b)(a-b)

If you multiply these factors together, you will arrive back at the original form a2-b2:

(a+b)(a-b) = a2 - ba + ba - b2 = a2-b2

For you example problem:

4x2-49

"a" is 2x, and "b" is 7, meaning:

4x2-49 = (2x)2-(7)2 = (2x+7)(2x-7)

Thus:

4x2-49 can be factored to (2x+7)(2x-7).

Answer 3

There is a formula for the "difference of squares." In this case, the answer is

(2x + 7)(2x - 7)