Simplify (a+b)^c | No Squareroot Needed

[GlobalDuty]

what is another way to form (a+b)^c to another simple expression?
like for example a^c+b^c doesn't work because its not eqivalent to (a+b)^c
(without using squareroot)

 

[mathwonk]

im know of no way that is simpler. just look at the example of (a+b)^100.

how simple is that? or just try to simplify (a+b)^3.

 

[CRGreathouse]

I occasionally find it useful to write it as a^c * (1 + b/a)^c -- of course only when working over the reals.

 

[GlobalDuty]

it doesn't have to be simpler, just not so complicated. thanks CRGreathouse, that helps,

 

[blue_raver22]

One possible way to form (a+b)^c to another simple expression without using square root would be to use the binomial theorem. This states that (a+b)^c can be expanded as the sum of the coefficients multiplied by each term raised to the appropriate power. For example, (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3. This can be simplified further by combining like terms, resulting in a simpler expression.