Question

How do you factor `4q^2 - 49`?

Answer 1

`4q^2-49 = (2q-7)(2q+7)`

Explanation:

The difference of squares identity can be written:

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

In our example, both `4q^2 = (2q)^2` and `49 = 7^2` are perfect squares. So the difference of squares identity works immediately with `a=2q` and `b=7` as follows:

`4q^2-49 = (2q)^2-7^2 = (2q-7)(2q+7)`