FoM: Chapter 3, Question 25, Drill 5

[ammanb875]

Simplify the following expression by pulling out as many common factors as possible

25) 6^3+3^3

My answer:
I pulled out the 3^3, so you get 3^3(2+1)
3^3(3)
3^4

The answer in the book was 3^5
The main difference being breaking down the 6 intp prime factors of
(2x3)^3
= (2^3)(3^3)+3^3
=3^3 (2^3+1)
= 3^3 (9)
= 3^5

I'm probably just missing something or made a careless mistake but if anyone can help me make sense of why you had to break down the prime factor and how it led to the difference in getting 3^4 vs 3^5 I would appreciate it. Thanks!

[Sage Pearce-Higgins]

Thanks for laying out your working so clearly. Yes, you're making an error in the factorizing stage:

6^3+3^3
I pulled out the 3^3, so you get 3^3(2+1)
3^3(3)
3^4

If I add an extra step, then
6^3+3^3 = (2^3)(3^3) + 3^3
Now factorize:
= 3^3(2^3 + 1)
= 3^3(9)

It looks like you forgot some "2"s and missed that 6^3 = (2^3)(3^3)