I learned multiplying a polynomial by a monomial this week. When there is a single term in polynomial, we call it monomial. Like these —> 2, 5, x, y, 5x, 8y, 4xy, 9yx, 7ab, 18xy

What I’m going to talk about now is multiplying the monomial by a polynomial.

• For example for this:  3a(a+1)

I’ll show you two ways to find the result of this.

FIRST WAY

As we learned in the first unit, exponents are always added during multiplication. I can hear you say there is no exponent here. But of course there is a hidden 1 above the a’s. So our polynomial looks like this —> 3a¹ (a¹ +1)

And now all we have to do is multiply monomal by terms.

And this is our result —> 3a²+3a¹  

And since most of the time we don’t show the exponent of a number whose exponent is one, our polynomial will look like this: 3a²+3a

SECOND WAY

In our second way, we will use algebra tiles.

Those are our algebra tiles. Now all we have to do is to place the two polynomials that we will multiply, just like in the multiplication table.

We can find it easily as we see above. The top 3 rectangles represent 3a, so each a represents a rectangle. On the far left, the rectangle represents a and the small square represents 1. And now all we need to do is draw the algebra tiles from the beginning to the tip of the algebra tiles on the top and side. Finally, we will either add or subtract the resulting algebra tiles according to the polynomial.

Another example: -x (5x-5y)

Now we know how to do it both ways. We can choose the path we want and do it that way. This time I’ll do it the first way.