## 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.

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

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

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

## 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.

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.

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.

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