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.
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.