When asked to factor this problem, a lot of students recognize there is a number that multiplies into both terms. A lot of students look at this, and they can already see that the greatest common factor is going to be 8.
So what most students will do is write this down, and they'll say I'm done. You guys this problem can actually be factored further. Look here.
This is what we call the difference of perfect squares. I can rewrite this as x minus 4, times x plus 4. The reason why is, because difference of perfect squares is when you see something that looks like this, two things that are squared like we had x² and 4², then you can write it out in factored form; like a minus b, a plus b.
So be careful when you're doing your factoring problems. A lot of times when students see a binomial that has two terms, they think they're done. But sometimes binomials can be factored even further into two more binomials.
It's really tricky. You'll get the hang of it when you do more practice, but this is the final answer. This is the most completely factored form of that original statement.
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