One of the first homework sets you guys are going to have when it comes to multiplying polynomial, is going to deal with monomials which look like this. Multiply 3x² times 5x to the forth. Well the way I approach this is to think of the constant terms first and then the x terms.
So 3 times 5 gives me 15, that’s going to be the first part of my answer and then x² times x to the forth be really careful it’s not x to the eighth, x² time x to the forth is x to the sixth. That’s the answer to my first problem. If you forget exponents or maybe haven’t studied that yet, try writing this out. 3x² looks like that. I’m multiplying it by 5x to the fourth, it looks like that so I have 15 and then x to the sixth. Be really careful that this is not x to the eighth. That’s going to be one of the trick questions that will show up like on your multiple choice test.
Let’s look at this next one. It’s trickier because it involves fractions and also it has 2 letters. Just be careful you’re going to multiply the regular numbers or constants first, then you multiply the Xs and then you multiply the Ys, so here we go. 1/3 times 12 is 4, x² times x is x to the third, and then last but not least y times y² is y to the third. There we go, that was two ugly monomials that I multiplied together.
Lastly I want to show you guys what it looks like when you distribute a monomial times some other polynomial. This is going to be really common if not in your homework then certainly on your test. This 5x has to get multiplied by this first term, this second term and the third term. It gets distributed across all of those pieces. So 5x times 3x² is 15x to the third. 5x times -2y is going to be -10, those are the numbers, and then I have an x and a y. And then last 5x times -4 is going to be -20x.
You guys should be getting super, super high scores on these homework problems and tests as long as you’re keeping track of the negatives. I’m going to say this over, and over, and over again. The only place where students lose points on these kinds of problems is if they lose a minus sign like that. You have to be really careful to keep track of your negatives and positives when it comes to multiplying polynomials.
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