How do you factor #64x^2 + 112x + 49#?

1 Answer
Jun 8, 2016

Answer:

#(7x+8)^2#

Explanation:

The key to factoring this is noticing that the first and last terms are both squared terms:

  • #64x^2=(8x)^2#
  • #49=(7)^2#

This is a good indicator that the expression is a perfect square binomial, which comes in the form:

#(a+b)^2=(a+b)(a+b)=a^2+2ab+b^2#

Here, #a=8x# and #b=7#, as indicated to us by the #64x^2# and #49# terms. However, we still have to determine whether or not the middle term #112x# is equal to #2ab#.

#2ab=2(8x)(7)=112x#

Since #2ab# does equal #112x#, we know that this is a perfect square binomial.

#64x^2+112x+49=(7x+8)^2#