Ma

Let's take the 1st expression:

**a**^{7}b^{8}+a^{5}b^{6}-a^{3}b^{2}

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:

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

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.