Find each product. See Examples 3–5. (m-n+k)(m+2n-3k)

Question

Accepted Answer

Hello today we're going to be performing the indicated multiplication. So what we are given is the quantity A plus B minus C. Times the quantity to a minus three B plus four C. Now in order to multiply these quantities together, we're essentially going to have to foil two quantities involving three terms each. So the way we start that process is we're going to first foil the term A. To each term in the second group. So foiling A. With two A is going to give us two A squared. Next A times negative three B is going to give us negative three. A. B. E. Times positive four C. Is going to give us positive for A C. And we're going to repeat this process with the next two terms in the first group. So next we're going to foil B with two A B times two A is going to give us positive to a B. Next be times negative three B. Is going to give us negative three B squared and finally be times four C. Is going to give us positive for B. C. And finally we're going to foil the final quantity which is negative C. So negative C times two A is going to give us negative two A C. Negative C. Times negative three B. Is going to give us positive three Bc and finally negative C. Times positive four C. Is going to give us negative four C squared. So after foiling these two quantities together, what we are left with is this jumble of terms however we can simplify this by combining like terms together. So for instance if we take a look at the A. B terms, we can combine three negative three A. B. With positive to a B. We can combine positive for A C. With negative two A. C. And finally we can combine positive for B. C with positive three Bc. Now let's go ahead and first start by writing down the terms that cannot be combined with any other and that's gonna be r squared quantities which is two A squared negative three B squared and negative four C squared. So we're going to start the simplified form as two A squared minus three B squared minus four C squared. And now we're going to write the A. B term. Next negative three. A B plus to A B. Is going to give us negative A B. Next we're going to write the bc terms and positive for B. C. Plus three Bc is going to give us positive seven Bc. Finally we're going to combine the A. C terms together and for a c minus to a C. Is going to give us positive to a C. 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 a 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. See Examples 3–5. (m-n+k)(m+2n-3k)

Key Concepts

Polynomial Multiplication

Like Terms

Distributive Property

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