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This problem is stressing me out

Factor the polynomial completely.
 
8a6b−18a4b
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1 Answer

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.
8a6b−18a4b
 
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(4a6b-9a4b)
 
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 4a6b there are 6 a's and in the term -9a4b 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 a4. When you factor out variables, subtract the exponents.

2a4(4a2b-9b)

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

2a4b(4a2-9)

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: a2-b2=(a+b)(a-b)
2. a2+2ab+b2=(a+b)(a+b)
3. a2-2ab+b2=(a-b)(a-b)

NOTE: The sum of two perfect squares CANNOT be factored. That is a2+b2 cannot be factored.

Now back to your question...

2a4b(4a2-9) For 4a2-9, the square root of 4a2 is 2a; the square root of 9 is 3

2a4b(2a+3)(2a-3)

Hope this helps you understand the process.