Question

I need to multiply these two binomials together: (x-2)(x-1). Please explain how to do them as well. Thanks!

Answer 1

There are 2 methods of completing this problem: FOIL and double distribution. They both will come up with the same answer, and will show you both methods.

FOIL:

FOIL stands for First, Outer, Inner, and Last and they are the positions within the binomials. Here is how to do that:

Firsts - the 1st term of each binomial - x * x = x^2

Outer - the ones on the outside of the binomial group - x * -1 = -x

Inner - ther terms that are closest to the inside parenthesis - -2 * x = -2x

Lasts - The last term in each binomial - -2 * -1 = 2

Now add them together: x^2 -x - 2x + 2 = x^2 -3x + 2 (Final answer)

Double distribution:

(x - 2)(x - 1)

x(x - 1) - 2(x - 1) (Distribute the (x -1) across the 1st binomial

x^2 - x - 2x + 2 (Distribute again for each set of terms)

x^2 - 3x + 2 (Simplify)

Answer 2

first multiply the second parenthesis by x then by -2:-

(x - 2)(x - 1)

= x(x - 1) - 2(x - 1)

= x^2 - x - 2x + 2

= x^2 - 3x + 2