Find each product.

Question

Find each product.

x^{2} (3 x - 2) (5 x + 1)

Accepted Answer

Hello. Today we're going to be performing the given multiplication. So what we are given is B squared times the quantity five B minus three times the quantity seven B plus eight. Now in order to perform the multiplication, we're going to need a first distribute B squared into the quantity five B minus three. And that means that we're going to multiply every term in the first quantity by B squared. So b squared times five B is going to give us five B to the third. Next b squared times negative three is going to give us negative three B squared. And that's gonna be the new first quantity with B squared distributed into it. But we're still taking the product of five B cubed minus three B squared times seven B plus eight. Now in order to multiply these quantities together, we're going to have to foil them together. So in order to foil them we're going to first take five B cubed and multiply it to seven B. Five b cubed times seven B. Is going to give us 35 B. To the fourth. Next five b cubed times positive eight is going to give us positive 40 B cubed. Next we're going to take the second term of the first quantity negative three B squared and foil it to the second quantity. So negative three B squared times seven B is going to give us negative 21 B cubed and finally negative three B squared times eight is going to give us negative 24 B squared. Now we can go ahead and simplify this product because the 2nd and 3rd term, our combined Herbal as they both have B to the power of three. So if we combine the middle two terms together, what we end up with is 35 B to the fourth plus 40 B cubed minus 21 B cubed. Which is going to give us positive 19 B cubed minus 24 B squared. And this is going to be the product in its simplest form. And with that being said, the answer to this problem is going to be C. So I hope this video helps you in understanding how to perform this multiplication and I'll go ahead and see you all in the next video.

Find each product. $x^{2} (3 x - 2) (5 x + 1)$

Key Concepts

Polynomial Multiplication

Distributive Property

Combining Like Terms

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