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.(4x+3)(5x+1)

Accepted Answer

Hey, everyone in this problem, we're asked to use the foil method of multiplication to find the product of the following binomial. Now, we're given the binomial seven H plus four, multiplied by the binomial 4h plus one. We have four answer choices. Option A 28 H squared plus 32 H plus four. Option B 28 H squared plus H plus four. Option C seven H squared plus H plus 16 in option D seven H squared plus 23 H plus 16. We're gonna start by rewriting the expressions we're given. So we have the binomial seven H plus four and we're multiplying the binomial 4h plus one. We're asked to use the foil method and recall that the foil method stands for first, outside inside last. So what we're gonna do is we're gonna start by taking the first terms of each binomial and multiplying them. So the first term of the first binomial is seven h. The first term of the second binomial is 4h. So we have seven H multiplied by 4h. And that is gonna be our term that corresponds with first. So the F in foil next we take the outside and when we have our binomials multiplied together, the outside is going to be the leftmost and the rightmost term. So the outside term, it is going to be seven h from the first binomial multiplied by one from the second bin meal. Those are outside terms corresponds with the Owen foil. Now we move to the inside. OK? And the inside terms are gonna be the ones that are almost touching. OK. So we're gonna take the four from the first binomial multiplied by the 4H from the second binomial. And this corresponds to our inside terms. Maybe the eye and foil. What we have left to do is the L and L corresponds for last. So we're gonna take the last term from our first binomial plus four, multiply it by the last term of the second binomial plus one, we have four multiplied by one which corresponds to our last terms. So now we've done the multiplication. We just need to simplify, we have seven H multiplied by 4h, starting with the constant coefficients, we have seven multiplied by four. So we know the coefficient is going to be 28 and we have H multiplied by H. When we multiply with the same base, we add the exponent. So we get H to the exponent one plus one. Simplifying our outside term seven H plus one Or sorry, seven h multiplied by one Gives us seven h OK plus our inside term four multiplied by 4h. This gives us 16 H And finally, our last terms, four multiplied by one, which gives us four, we can simplify a little bit more, we can simplify our exponent. OK. So 28 H to the exponent one plus one is going to become 28 H squared, We have seven h plus 16 h. So we can combine those, this is gonna give us In our final term plus four. So we have an H squared term, an H term and a constant term. We can't simplify any further. And so this is our final result. OK. We found that using the foil method of multiplication, the product of our binomials is 28 H squared plus 23 H plus four, which corresponds with answer choice B 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.(4x+3)(5x+1)

Key Concepts

Binomials

FOIL Method

Combining Like Terms

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