Question

Use FOIL to explain how to find the product of(a + b)(a - b). Then describe a shortcut that youcould use to get this product without using FOIL.Which facts did you include in your reCheck all of the boxes that apply.Multiply the first, outside, inside,terms of the binomials.a/2-b/20Multiply a times a, a times -b, b tinb times -b.COMELETEThis is the same as just squaring aSquaring b.OA shortcut is to add a squared andDONE

Answer 1

SOLUTION

First, let us use the FOIL method to expand the binomial.

$\left(a+b\right)\left(a-b\right)$

The FOIL method means

F- we multiply the first terms together. The first terms are a and the other a, we have

$a\times a=a^2$

O - we multiply the outside terms, which are a and the other -b, we have

$a\times-b=-ab$

I - we multiply the inside terms. The inside terms here are b in the first part and a in the second part, we have

$b\times a=ab$

And lastly we multiply the last terms which are b and -b, we have

$b\times-b=-b^2$

Combining all we have

$a^2-ab+ab-b^2$

The short cut we can use, we say

$\begin{gathered} \left(a+b\right)\left(a-b\right) \\ a\left(a-b\right)+b\left(a-b\right) \\ that\text{ is using the first two terms to multiply the second two terms} \\ we\text{ have } \\ a^2-ab+ab-b^2 \end{gathered}$

So the facts I included in my response are

Multiply the first, outside, inside and last terms of the binomial (the FOIL method).

Multiply a times a, a times -b, b times a and b times -b (the short cut).

Hence the first and second options are the answers