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.

(y − 5)²

Accepted Answer

Hey, everyone in this problem, we're asked to perform multiplication on the given expression. The expression we're given is M -11 all squared. We're given four answer choices. Option AM squared plus 11 M minus 121. Option B M squared minus 11 M plus 121 C M squared plus 22 M minus 121. And option D M squared minus 22 M plus 121. We're gonna rewrite the expression we're given. So we have M -11 in brackets squared and recall that we, we have an expression squared, we can write this as M minus multiplied by M -11. OK. These are equivalent and now that it's in this form where you have one binomial multiplied by another binomial, we can use our foil method. So we're called the foil method which tells us to multiply the first terms, the outside terms, the inside terms and then the last terms in our expression in order to expand. So applying this, we're gonna start with our first terms. So the first term from this first binomial is M and the first term from the second binomial is M as well. And so we have M multiplied by M and this represents our first terms or the F and foil. Now, we can move to the outside terms. So the furthest outside terms, so the far left and the far, right. So on the far left of our expression, we have M and on the far right of our expression, we have negative 11. So we have M multiplied by -11. This represents our outside terms or the O and foil. And again, then we add, and the next term in this expansion is going to be the inside terms. So we're gonna take the innermost terms, we took the outermost terms that were furthest away. Now we're gonna take the innermost terms that are closest together from the first expression. We have negative 11. And from the second, we have M, we have negative 11 multiplied by M which is our inside terms, the eye and foil and we add one more time and we're gonna take the last terms this time. So the last term from the first binomial is negative 11. The last term from the second binomial is also negative 11. And so we have negative 11 multiplied by -11. These are our last terms for the L and foil. So now we've done that multiplication, we have the four terms of the resulting expression. And we're left just to simplify. So we have M multiplied by M. Recall that if we multiply two things with the same base, we add the exponents. So this becomes M to the exponent one plus one. We have M multiplied by -11. It's gonna give us -11. MS again, negative 11 times M, we have negative 11 M in our final term, -11 multiplied by -11. That's gonna give us positive 121. And so we have our expression M to the exponent one plus one minus 11 M minus 11 M plus 121. We have one more step that we can simplify. First thing we can do is simplify the exponent in this first term M to the exponent one plus one gives us M squared. Then we have minus 11 M minus 11 M and we can combine those two terms. And that's gonna give us -22 m and R Plus 121 that constant at the end. So now we have an M squared term, an M term and a constant term. We can't simplify any further. And so this is the resulting expression we were looking for comparing this to our answer choices. We found that when we performed multiplication, we got the expression M squared minus 22 M plus 121 which corresponds with answer choice. D. 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. (y − 5)²

Key Concepts

Binomial

Square of a Binomial

Algebraic Expansion

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