HI! i'm going to talk about difference of squares. As you can see in the picture, factoring difference of squares is very easy. You just have to know your perfect squares and there's no doubt, you can do difference of square in just a second. =))

a² - b²

This expression is called DIFFERENCE OF TWO SQUARES.

(a+b) (a-b) = a² - b²

How about this one? You may remember seeing expressions like these one when you worked with multiplying algebraic expressions.

If you know this fact, then you already know that the factors of

are

(a - b) (a +b)

REMEMBER: An algebraic term is a perfect square when the numerical coefficient (the number in front of the variables) is a perfect square and the exponents of each of the variables are even numbers. =)

EXAMPLES:

1. Factor x² - 9

Both x² and 9 are perfect squares. Since subtraction is occurring between these squares, this expression is the difference of two squares.
What times itself will give x² ? The answer is x.
What times itself will give 9 ? The answer is 3.
These answers could also be negative values, but positive values will make our work easier.
The factors are (x + 3) and (x - 3).Answer: (x + 3) (x - 3) or (x - 3) (x + 3)

2. Factor x⁴ – 1

So the square root of x⁴ is x² and the square root of 1 is 1. So you'll end up with (x²-1) (x²+1).
As you can see, we're not done yet. We can still factor x²-1 into (x-1)(x+1).
Now it's completely factored.
So the answer'll be (x-1)(x+1)(x²+1)



So now that I've explained what difference of squares is, maybe you want to try more exercises to master your factoring skills. So that's it. That's how easy factoring of difference of squares is. In my opinion, its the easiest and fastest factoring method. So, enjoy! =)

-janelle :)