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Numerade Educator

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Problem 7 Medium Difficulty

Perform the indicated operations.
$$-9 m\left(2 m^{2}+3 m-1\right)$$

Answer

$-9 m\left(2 m^{2}+3 m-1\right)=-18 m^{3}-27 m^{2}+9 m$

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Video Transcript

So we are going to perform the indicated operation of the following expression Negative nine M parentheses to M squared plus three M minus one close parentheses. The parentheses here are functioning as, ah, multiplication symbol, and they're also functioning as a grouping symbol. So what we know is that this entire expression here is being grouped together and we want to multiply that entire group by negative nine em. And so the way that we're going to multiply that entire group by negative nine m is by applying the distributive property of multiplication over addition. So I'm going to distribute the negative nine m which with each one of these terms here. So the negative nine m is gonna multiply by the first term, the second term and also the third term. So I'm gonna start by taking negative nine m and multiplying in by two and squared. Then I'm gonna take the negative nine m and multiply it by the positive three in Finally, I'm gonna take the negative nine m and multiply it by the negative one. So now I'm going to perform each of these multiplication sze So when we multiply negative nine m times to m squared. We're gonna find that negative nine times two is negative 18 and m times m squared. That's like saying and times M squared, which is M times M that's gonna give me three m's being multiplied together. So that's gonna be an M cubed. And then I've got negative nine times three, which is negative. 27 m times m is m squared. And then finally, I've got negative nine times negative one. We remember that a negative times negative is a positive that's gonna be nine. And then there's a single m here. So nine em Now I've got a plus and then a negative number when we add a negative number. Essentially, what we're just doing is subtracting it. So the final answer to this problem is negative. 18 and cubed minus 27 and squared plus nine em