Hello class, yesterday we learned about factoring. There are 3 special cases of factoring

• Greatest common factor
• Difference of Perfect Squares
• Perfect Square Trinomials

Heres an example of a problem in which we need to solve using the Greatest Common Factor

5wz+25w^2(z)-35w^3(z)

First we need to find the GCF. All of the numbers are multiples of 5 so 5 would be a GCF so it would come outside the parentheses.

5(__________)

We can also see that every one of them has at least one w in it so that would also come outside the parentheses.

5w(_________)

We can also see that there is a z in every number so that too would come out of the parentheses and now you divide everything inside the parentheses by 5wz and your product should look like this

5wz(1+5w-7w^2)

Now heres an example problem with Difference of Powers Squared

x^2-1oo

the form for solving this kind of problem is a^2-b^2=(a+b)(a-b)

so we need to think. what times what equals x^2? well that would just be x

(x+__)(x-__)

Now what times what equals 100? well that would just be 10.

(x+10)(x-10)

and do not worry about the 10x and -10x because they cancel each other out.

And here is an example of a problem with perfect Square Trinomials. They are called that because the first and last numbers are perfect squares.

9x^2+6x+1

Now what times what equals 9x^2? 3x so,

(3x)(3x)

Now what times what equals 1? 1 so,

(3x+1)(3x+1)

and that is ok because when you distribute it 3x plus 3x equals 6x

Now we all know that something times itself is just that something squared so the final answer would look like this,

(3x+1)^2

I hope this blog is useful in understanding this concept. Thanks.

-Tim Kirby