Find each product. See Example 5.(3x + 1) (2x - 7)

Question

Accepted Answer

Hello, everyone. We are asked for the following polynomial expression to perform the indicated operations. To simplify the expression we are given is the parentheses eight Y plus five, multiplied by the parentheses. Five Y minus nine. Our answer choices are a 40 Y squared plus 47 Y minus 45 B Y squared plus 97 Y minus C 40 Y squared minus 47 Y minus 45 D 40 Y squared plus 97 Y plus 45. I'm gonna start by rewriting our expression. So we have parentheses eight Y plus five multiplied by the parentheses five Y minus nine. I recognize that these are both binomials. And I recall that when I multiply binomials, I use what we call the foil method boils an acronym for the order I'm gonna multiply in. So F stands for first. So this means I'm going to multiply my first terms together. So eight Y multiplied by five, Y eight multiplied by five is 40 Y multiplied by Y is Y squared. So for F, we have 40 Y squared, O stands for outer, so the outermost terms. So in this case, eight Y and negative nine. And when I multiply those two together, I get negative 72 Y. So that's my O term I is inner. So it's the innermost terms. So this will be five multiplied by five Y and multiplying those together, we get plus 25 Y and L stands for last. So the last term in each bin, no meal. So this would be five multiplied by negative nine, which is negative 45. So at this step, we have 40 Y squared minus 72 Y plus Y minus 45 we need to combine our lake terms. The O and I terms are the only ones that are like terms. So we're gonna combine those. So we have 40 Y squared combining negative Y and positive 25. Y will give us negative 47 Y minus 45 because that term did not change. So this trinomial is our answer 40 Y squared minus 47 Y minus 45 and that is answer choice C have a nice day.

Find each product. See Example 5.(3x + 1) (2x - 7)

Key Concepts

Distributive Property

Binomial Multiplication

Combining Like Terms

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