Hi Mike, I was wondering if you could explain a little bit better question 2 of the “Binomial Squares and Difference of Two squares” Practice questions. More particularly, I was wondering if there was a way to convert the equation to the right answer.

Thanks

You mean factoring the given expression rather than expanding the answer choices? Yes, that can be done. Here’s the original expression:

Note the patterns in the powers of *a* and *b*: you have , , and no *a* in the final term; you have no *b* in the first term, then *b* and . With enough experience looking at binomials, you might recognize that as a pattern that you’d expect to get when you FOILed something like this:

From there, recognize that you have perfect squares as coefficients in the first and third terms: 25 and 16. That’s pretty cool—let’s see if using 5 and 4 in the factored expression gives us what we want:

Yep, that’s what we were hoping for, so our factoring was correct. That means choice A is correct.