In Exercises 55–68, multiply using one of the rules for the squar...

Question

In Exercises 55–68, multiply using one of the rules for the square of a binomial.

(x + 3)²

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication on the given expression. The expression we're given is R plus 14, all squared. We have four answer choices. Option A R squared plus R plus B R squared plus 14, R plus 196 C R squared minus 28 R plus 196 and D R squared minus 14 R plus 196. We're gonna start by rewriting the expression we're given. So we have the Binomial R plus 14 and it is squid and recall that when we have this type of expression squared, we can just rewrite this as the binomial R plus multiplied by the binomial R plus 14. And these two are equivalent. And when we have two binomials multiplied together like this, this looks a little bit more familiar and we can apply our foil method. So we call the foil method, OK to get those four terms of the resulting expression. When we multiply two binomials, we take the first terms multiply them together, then the outside terms multiply them together, then the inside terms multiply them together and then the last terms and multiply them together and we add those four terms up to get a resulting expression. So if we apply the foil method to this expression, we're gonna start with the first term. So the first term from the first binomial is R, the first term from the second binomial is R. So we have R multiplied by R and this represents our first terms or the F in foil. And then we add the next terms we're gonna take are the outside terms. So we're gonna take the term on the far left and the term on the far, right. So from the first expression on the far left, we get R from the second binomial on the far right, we have 14. So we have R multiplied by and this represents our outside terms or the O and foil. Then we add, we move to the next term. The next term is gonna take the inside terms. OK? So we've done the two outsides the furthest away. Now we're gonna take the two terms in the middle. So from the first binomial, we have 14 and from the second binomial, we have R, so we have 14 multiplied by R. These are inside terms here are the iron foil. And then we add, and we're gonna add our last term, which is gonna be made up of last terms. So we're gonna take the last term of the first binomial multiply it by the last term of the second binomial. And we're gonna have 14 multiplied by 40. This represents our last terms or the L in foil. So now we've done the multiplication, we've expanded this expression and all that's left to do is simplify, starting with our first term. We have R multiplied by R I recall when we have two things multiplied together with the same base, we add the exponents. So we have R to the exponent one plus one plus R multiplied by 14. And this gives us 14, R plus 14, R again, OK? 14 multiplied by R plus 14, multiplied by 14, 196. And one thing I wanna point out is these two inside terms or the two middle terms I should call them. So the outside term and the inside term those are equal. OK? And they're equal because we have our expression squared, our binomial squared. OK? So those two middle terms the in outside and inside terms will be the same when you have a binomial squared like this. So we wanna simplify one more step. We have R to the exponent one plus one. We can write this as R squared. OK? And then we're gonna add, we have 14 R plus 14 R. So we can combine these, we have 28 r plus our constant term 196. Now we have an R squared term, an R term and a constant term. This expression is as simplified as we can get it. And so this is the result we were looking for. If we compare this to our answer choices, we found that when we multiply the expression we're given, we get R squared plus 28 R plus 196 which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 55–68, multiply using one of the rules for the square of a binomial. (x + 3)²

Key Concepts

Binomial

Square of a Binomial

Algebraic Expansion

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