Hi Candice,

Wouldn't want you to be stress out so let's see if we can figure this problem out.

Factor the polynomial completely.

8a^{6}b−18a^{4}b

First we look for a greatest common factor that can be factored out of the binomial expression.

The two coefficients are 8 and -18. What is the greatest factor that divides into them evenly?

Both numbers are divisible by 2

2(4a^{6}b-9a^{4}b)

Now let's look at the variable a. The question you need to ask is what is the greatest number of a's that can be factored out? In the term 4a^{6}b there are 6 a's and in the term -9a^{4}b there are 4 a's, so the greatest number of a's common to both terms is 4 a's. So you can factor out a^{4}. When you factor out variables, subtract the exponents.

2a^{4}(4a^{2}b-9b)

Can any b's be factored out? YES. There is one b common to both terms.

2a^{4}b(4a^{2}-9)

Our next question is whether the remaining binomial be factored.

There are three common factoring formulas that are good to memorize when factoring polynomials.

The three formulas are:

1. The difference between two perfect squares: a^{2}-b^{2}=(a+b)(a-b)

2. a^{2}+2ab+b^{2}=(a+b)(a+b)

3. a^{2}-2ab+b^{2}=(a-b)(a-b)

NOTE: The sum of two perfect squares CANNOT be factored. That is a^{2}+b^{2} cannot be factored.

Now back to your question...

2a^{4}b(4a^{2}-9) For 4a^{2}-9, the square root of 4a^{2} is 2a; the square root of 9 is 3

2a^{4}b(2a+3)(2a-3)

Hope this helps you understand the process.