a3 + b3 = (a + b)(a2 - ab + b2)
a3 - b3 = (a - b)(a2 + ab + b2)
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There is a formula for the difference of two squares. The sum of two squares doesn't factor.
a^3 + b^3 = (a + b)(a^2 - ab + b^2) a^3 - b^3 = (a - b)(a^2 + ab + b^2)
The answer will depend on what you mean by "do the sum". Why not simply add them together? For example 93 = 729 and 103 = 1000 so 93 + 103 = 729 + 1000 = 1729. NB: Totally irrelevant to the question, but the above example is the smallest integer that can be expressed as a sum of two positive cubes in two different ways - as Ramanujan was to inform the Cambridge (UK) mathematician Hardy.
Step 1. Look for a GCF. Step 2. Look for the difference of squares. ex: a2 - b2 = (a+b)(a-b) Step 3a. Look for the difference of cubes. ex: a3 - b3 = (a-b)(a2 + ab + b2) Step 3b. Look for the sum of cubes. ex: a3 + b3 = (a+b)(a2 - ab + b2)
That can't be factored. In general, a binomial (i.e., a polynomial with two parts) can only be factored if both parts have a common factor, or if you can express it as the sum or difference of squares, cubes, etc.