In Exercises 9–22, multiply the monomial and the polynomial.

3ab...

Question

In Exercises 9–22, multiply the monomial and the polynomial.

3ab² (6a²b³+5ab)

Accepted Answer

Hello, everyone. We are gonna perform multiplication for the given monos. We are given nine P cubed Q multiplied by the parentheses. Five P Q plus three P squared. Q raised to the fifth power. Our answer choices are a 27 P raised to the fourth power Q squared plus 45 P raised to the fifth. Power Q raised to the sixth power B 45 P raised to the fourth power Q squared plus 27 P raised to the fifth power Q raised to the sixth power C 45 P cubed Q squared plus 27 P raised to the fifth. Power Q raised to the sixth power D 27 P cubed Q squared plus 45 P raised to the fifth power QQ raised to the sixth power rewriting my original multiplication. I have 9 p cubed Q multiplied by open parentheses. 5 PQ plus three P squared. Q raises to the fifth power, close parentheses. I'm going to multiply the number outside of the parentheses into both terms in the parentheses. So I'll be distributing, I'm gonna start off by doing nine P cubed Q multiplied by five P Q I recall that when I multiply mono meals, I start by multiplying the coefficients nine, multiplied by five is 45. And then I want to multiply my like bases. I also recall that any variable that doesn't show me the exponent automatically has an exponent of one. So when I do P cubed times P, that's the same as saying P cubed multiplied by P to the first, our base of P stays the same and we add our exponents. So we get P raised to the fourth power. Next, like base would be Q. So I have Q raised to the first power multiplied by Q raised to the first power. One plus one is two. So I have Q squared. So my first term is 45 P raised to the fourth power Q squared. Next, I need to do nine P cubed Q multiplied by three P squared. Q raised to the fifth power. Again, I'm gonna start with my coefficients nine multiplied by three. They're both positive. So this is gonna be a positive P cubed multiplied by P squared. The base of P stays put three plus two is five. So we have P raised to the fifth power, then Q multiplied by Q raised to the fifth power. So Q to the first multiplied by Q to the fifth will give me Q to the sixth power. So we get 45 P raised to the fourth power Q squared plus 27 P raised the fifth power. Q raised the sixth power which is answer choice B have a nice day.

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In Exercises 9–22, multiply the monomial and the polynomial. 3ab² (6a²b³+5ab)