Factor the GCF out of this given expression:Please explain the steps on you got it so as i can practice with it for future similar problems

(1) a^7b^8+a^5b^6-a^3b^2

(2) -18a^5-30a^3+24a^2

(3) 6x(x-8)-5(x-8)

HELP ME OUT PLEASE SOLVE IT WITH FACTOR

Factor the GCF out of this given expression:Please explain the steps on you got it so as i can practice with it for future similar problems

(1) a^7b^8+a^5b^6-a^3b^2

(2) -18a^5-30a^3+24a^2

(3) 6x(x-8)-5(x-8)

Factor the GCF out of this given expression:Please explain the steps on you got it so as i can practice with it for future similar problems

(1) a^7b^8+a^5b^6-a^3b^2

(2) -18a^5-30a^3+24a^2

(3) 6x(x-8)-5(x-8)

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George T. | George T.--"It's All About Math!"George T.--"It's All About Math!"

Ma

Let's take the 1st expression:

Notice that all three of the terms have variables a and b raised to different powers. The Greatest Common Factor of GCF is determined by selecting the
**lowest **power for each variable across all of the terms.

Since **a**^{3} is the lowest power for the variable** a**, **a**^{3} becomes part of the GCF.
**Another way to look at it is that a**^{3} is the highest factor that is common or present in all three terms (hence the terminology GCF).

Since **b**^{2} is the lowest power for b, **b**^{2} becomes part of the GCF.

Putting this all together, the GCF is therefore **a**^{3}b^{2}.

By factoring out the GCF, the original expression can be re-written as **
a**^{3}b^{2}(a^{4}b^{6}+a^{2}b^{4}-1).

Now let's look at the 2nd expression:

For the three constants -18, -30, and 24 shown in the 3 terms, the GCF is **
6**, since 6 is the greatest number divisible into all three.

For the variable **a,** the GCF is **a**^{2}, since a^{2} is the lowest power for variable a. Another way to look at it is that
**a**^{2} is the highest factor that is common or present in all three terms (hence the terminology GCF)

Putting this all together, the GCF is **6a**^{2}.

By factoring out the GCF, the original expression can be re-written as **
6a**^{2}(-3a^{3}-5a+4).

See William's answer above to the third expression. As he notes, there are no common factors across the three terms of the resulting expression.

Let me know if this helps.

George T.

1. a^{7}b^{9} + a^{5}b^{6} - a^{3}b^{2}

For the moment, don't think of a^{7} as being a^{7}, rather (a^{3})(a^{4})

(a^{3})(a^{4})b^{9} + a^{5}b^{6} -a^{3}b^{2}

Similarly, don't think of a^{5} as being a^{5}, rather (a^{3})(a^{2})

We are left with

Thus, a^{3} is part (but only part) of our GCF.

Let's go through a similar process with the b term: b^{9} = (b^{2})(b^{7}) and b^{6} = (b^{2})(b^{4})

Substituting

and we have successfully factored out our GCF. (in bold print)

2. -18a^{5}-30a^{3}+24a^{2}

Rewrite:

-**(2)(3)**(3)**(a**^{2})(a^{3}) -
**(2)(3)**(5)**(a**^{2})(a) + **(2)(3)**(4)**(a**^{2})

3. 6x(x-8)-5(x-8) ⇒ 6x^{2} - 48x - 5x + 40

6x^{2} - 53x + 40

This is one of those expressions for which there is no GCF.

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