Factor the expression 36a^4^10 - 81a^16b20 using the two different techniques listed for Parts 1(a) and 1(b).

Question

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

Answer 1

(a) Factor the expression using the GCF monomial:

The greatest common factor (GCF) of 36a^4^10 and 81a^16b^20 is 9a^4. This means we can factor out 9a^4 from both terms:

36a^4^10 - 81a^16b^20
= 9a^4(4a^6 - 9a^12b^20)

(b) Factor the expression using the difference of squares:

The expression can be rewritten as a difference of squares by noticing that 36 = 6^2 and 81 = 9^2:

36a^4^10 - 81a^16b^20
= (6a^2)^2 - (9a^8b^10)^2
= (6a^2 - 9a^8b^10)(6a^2 + 9a^8b^10)
= 3a^2(2a^2 - 3a^8b^10)(2a^2 + 3a^8b^10)