Wednesday, November 15, 2017

Middle School Math Solutions – Expand Calculator, Perfect Squares

The perfect square formula is an application of the FOIL method that will help you calculate the square of a binomial quickly.

Let’s take a look at the formula:

                                                     (a+b)^2=a^2+2ab+b^2

Here’s the proof:

                                                    (a+b)^2=(a+b)(a+b)
                                                                   =a^2+ab+ab+b^2
                                                                   =a^2+2ab+b^2

Now, let’s see some examples using the perfect squares formula.

First example (click here):

                                                         Expand (x+1)^2

1. Apply the formula

                                                              a=xb=1

                                                 (x+1)^2=x^2+2∙x∙1+1^2
                                                                =x^2+2x+1

Second example (click here):

                                                         Expand (5-x)^2

1. Apply the formula

                                                             a=5b=-x

                                             (5-x)^2=5^2-2∙5∙(-x)+(-x)^2
                                                            =25+10x+x^2

Last example (click here):

                                                      Expand (s^2+4p)^2

1. Apply the formula

                                                            a=s^2, b=4p

                                        (s^2+4p)^2=(s^2)^2+2∙s^2∙4p+(4p)^2
                                                           =s^4+8s^2 p+16p^2

The more you practice these problems, the faster you will be able to do them. I’ve used this formula so much, that now, I don’t need it since I can do it all mentally. For more help or practice on this topic, check out Symbolab’s Practice.

Until next time,

Leah

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