# Special Products Question

• March 20th 2008, 03:54 AM
Silverwolph
Special Products Question
This is the problem:

(2^m+1)^2
by the special product rules it equals
4^(mm)+4^m+1
but if I plug in 2 as m then
(2^2+1)^2=25 but 4^4+4^2+1 does not equal 25

could someone please explain why this will not check
• March 20th 2008, 05:00 AM
mr fantastic
Quote:

Originally Posted by Silverwolph
This is the problem:

(2^m+1)^2
by the special product rules it equals
4^(mm)+4^m+1
but if I plug in 2 as m then
(2^2+1)^2=25 but 4^4+4^2+1 does not equal 25

could someone please explain why this will not check

Isn't it obvious ...... $(2^m + 1)^2 \neq 4^{mm} + 4^m + 1$.

Using the ordinary product rule:

$(2^m + 1)^2 = 2^{2m} + 2^{m+1} + 1 = 4^m + 2^{m+1} + 1$.