Factor the expression 36a^4(b^10) - 81a^16(b^20) using the two different techniques listed for Parts 1(a) and 1(b).

(a) Factor the given expression using the GCF monomial.
(b) Factor the given expression using the difference of squares

1 answer

(a)
First, find the greatest common factor (GCF) of the terms:
GCF = 9a^4(b^10)

Now divide each term by the GCF:
36a^4(b^10) / 9a^4(b^10) = 4
81a^16(b^20) / 9a^4(b^10) = 9a^12(b^10)

So the factored expression using the GCF monomial is:
9a^4(b^10)(4 - 9a^12)

(b)
The given expression can be expressed as a difference of squares:
36a^4(b^10) - 81a^16(b^20) = (6a^2b^5)^2 - (9a^8b^10)^2

Now, using the formula for the difference of squares: a^2 - b^2 = (a + b)(a - b), the expression can be factored as:
(6a^2b^5 + 9a^8b^10)(6a^2b^5 - 9a^8b^10)