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

Question

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)

Answer 1

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 a, a³ 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.

 

 

 

 

 

Answer 2

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.