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HELP ME OUT PLEASE SOLVE IT..............

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)
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2 Answers

Ma
 
Let's take the 1st expression:
 
a7b8+a5b6-a3b2
 
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 a3 is the lowest power for the variable aa3 becomes part of the GCF.  Another way to look at it is that a3 is the highest factor that is common or present in all three terms (hence the terminology GCF).
 
Since b2 is the lowest power for b, b2 becomes part of the GCF.
 
Putting this all together, the GCF is therefore a3b2.
 
By factoring out the GCF, the original expression can be re-written as a3b2(a4b6+a2b4-1).
 
 
 
Now let's look at the 2nd expression:
 
-18a5-30a3+24a2
 
 
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 a2, since a2 is the lowest power for variable a.  Another way to look at it is that a2 is the highest factor that is common or present in all three terms (hence the terminology GCF)
 
Putting this all together, the GCF is 6a2.
 
By factoring out the GCF, the original expression can be re-written as 6a2(-3a3-5a+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. a7b9 + a5b6 - a3b2
 
For the moment, don't think of a7 as being a7, rather (a3)(a4)
 
(a3)(a4)b9 + a5b6 -a3b2
 
Similarly, don't think of a5 as being a5, rather (a3)(a2)
 
We are left with
 
(a3)(a4)(b9) + (a3)(a2)(b6) - (a3)(b2)
 
Thus, a3 is part (but only part) of our GCF.
 
Let's go through a similar process with the b term: b9 = (b2)(b7) and b6 = (b2)(b4)
 
Substituting
 
(a3)(b2)(b7)(a4) + (a3)(b2)(b4)(a2) - (a3)(b2)
 
[(a3)(b2)][(a4b7) + (a2b6) -1]
 
and we have successfully factored out our GCF. (in bold print)
 
2. -18a5-30a3+24a2
 
Rewrite:
 
-(2)(3)(3)(a2)(a3) - (2)(3)(5)(a2)(a) + (2)(3)(4)(a2)
 
6a2 [4 - 3a3 - 5a]
 
3. 6x(x-8)-5(x-8) ⇒ 6x2 - 48x - 5x + 40
 
6x2 - 53x + 40  
 
This is one of those expressions for which there is no GCF.
 
 

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