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

1 Answer
Apr 21, 2016

Answer:

#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)#