Question

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

Answer 1

`(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`