In Exercises 35–54, use the FOIL method to multiply the binomials...

Question

In Exercises 35–54, use the FOIL method to multiply the binomials.

(y+5)(y−6)

Accepted Answer

Hey, everyone using the foil method of multiplication. What is the product of the following binomial? The binomials we're given are H plus seven, Multiplied by the 2nd Binomial H -8. We're given four answer choices. Option A H squared minus H minus 54. Option B H squared plus H minus 54. Option C H squared minus H minus 56 option DH squared plus H minus 56. We're gonna start by rewriting our binomials. So we have the first binomial H plus seven Multiplied by the 2nd Binomial H -8. And we're asked to use the foil method and what the foil method represents is first outside inside last. So we're gonna take the first two term, the first term from each of our binomials and multiply them. We're gonna take the outside terms multiply them. We're gonna take the inside terms and multiply them. And we're gonna take the last terms of each binomial and multiply them. And that's gonna give us the four terms of our resulting expression. OK. So let's do this. So starting with the first terms, the first term of the first binomial is H the first term of the second binomial is H, so we have H multiplied by H and again, this represents the first or the F in foil. Then we're gonna add, we're gonna add the outside terms. So we're gonna take the left, most outside term, the right, most outside term multiply them. We're gonna have H Multiplied by -8. This represents our outside terms or the O and foil. Then we're gonna add, and we're gonna add our inside terms. So the innermost terms when we have our two binomials multiplied together, we're gonna have seven from the first binomial and H from the second binomial. So we get seven multiplied by, this is our inside term or the I in foil, we have one more term, the last term. OK? So we're gonna take the last term of our first binomial seven and multiply it by the last term of our second binomial negative eight, Seven multiplied by -8. And this is our last term or the L in foil. So now we've applied the foil method. OK? And what we have left to do is simplify this expression. So for our first term, we have H multiplied by H recall when we have the same base and we multiply them together, we're gonna add the exponents. So this is gonna give us H to the exponent one plus one. For our outside term, we have H multiplied by negative eight. This is gonna give us negative eight. H So our expression is now H to the exponent one plus one minus eight H OK. Our inside term seven multiplied by H. So we're gonna add seven H to our existing expression in our last term seven multiplied by negative eight gives us negative 56. And so we subtract 56 from our expression, we can simplify a little bit further. So we can simplify the exponent on our first term. We have H to the exponent one plus one. This gives us H squared, we also have two H terms. We have negative eight H plus seven H. So we can combine those negative A H plus seven H gives us negative H. So we have H squared minus H minus 56. Then that's a resulting expression. We can't simplify that any further. We have an H squared term, an H term and a constant term. And that is what we were looking for. If we compare this to the answer choices we've been given using the foil method, we found that the product of the binomials was H squared minus H minus 56 which corresponds with answer choice. C Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 35–54, use the FOIL method to multiply the binomials. (y+5)(y−6)

Key Concepts

FOIL Method

Binomials

Combining Like Terms

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