^{6}b−18a

^{4}b

Factor the polynomial completely.

8a^{6}b−18a^{4}b

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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

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)

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

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.

2a

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

2a

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. a

3. a

NOTE: The sum of two perfect squares CANNOT be factored. That is a

Now back to your question...

2a

2a

Hope this helps you understand the process.

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