Tuesday, November 7, 2017

Middle School Math Solutions – Expand Calculator, Two Squares

The difference of two squares is an application of the FOIL method (refer to our blog post on the FOIL method).   The difference of two squares is a number or term squared subtracted from another number or term squared. We get it when we multiply two binomials, where the terms in the binomials are the same, except one of the terms is subtracted instead of being added.

Let’s see this in a formula:
                                                             (a+b)(a-b)=a^2-b^2

Here’s the proof using the FOIL method:
                                                      (a+b)(a-b)=a^2-ab+ab-b^2
                                                                                =a^2-b^2

Not too complicated, so let’s see some examples.

First example (click here):
                                                             Expand (x+2)(x-2)

1. Apply the formula
                                                                        a=x,b=2

                                                             (x+2)(x-2)=x^2-2^2
                                                                                       =x^2-4

This next one is a little more complicated.

Next example (click here):
                                                           Expand (-y+2x)(y+2x)

1. Rewrite the problem
                                                      (-y+2x)(y+2x)=(2x-y)(2x+y)
                                                                                      =(2x+y)(2x-y)

2. Apply the formula

                                                                    a=2x,b=y

                                                     (2x+y)(2x-y)=(2x)^2-y^2
                                                                                   =4x^2-y^2

For our last example, we will see an application of the difference of two squares formula.

Last example (click here):
                                                                        23∙17

1. Rewrite the numbers
                                                                (20+3)(20-3)

2. Apply the formula
                                                                     a=20,b=3

                                                          (20+3)(20-3)=20^2-3^2
                                                                                        =400-9
                                                                                        =391

As you can see, this formula is simple, but very helpful. If you need more help or practice with this formula, check out Symbolab’s Practice.

Until next time,

Leah

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