Question

Expand (x-2) (x-1). Must be in polynomial form.

Answer 1

To expand two terms such as these, we can use the method called FOIL (stands for First, Outer, Inner, Last). Here is what I mean:

We have two terms: (x - 2)(x - 1)

We should first multiply the First two terms of each term in order to complete the F stage:

(x)*(x) = $x^{2}$

So then, we take the two outer terms and multiply them together to complete the O stage:

(x)*(-1) = -x

So far we have two things that we have calculated; at the end of the FOIL process we will have four.

To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:

(-2)*(x) = -2x

Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:

(-2)*(-1) = 2

Now that we have our four terms, let us add them together and combine like terms:

$x^{2} + (-x) + (-2x) + 2$

Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:

-x + (-2x) = -3x

So now that we have our terms completed, we can combine into one polynomial equation:

$x^{2} + (-3x) + 2$ or $x^{2} -3x+2$