Q: Factor completely a2 ab 42b2

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a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)

(a3 + b3)/(a + b) = (a + b)*(a2 - ab + b2)/(a + b) = (a2 - ab + b2)

(a-b)2 = (a-b)(a-b). You have to multiply each term in the left monomial by each term in the right monomial: a2 - ab - ab + b2 = a2 - 2ab + b2.

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a3 - b3 = (a - b) (a2 + ab + b2)

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a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)

Sum and difference of two cubes is factored this way : a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)

a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2

a3 + b3 = (a + b)*(a2 - ab + b2)anda3 - b3 = (a - b)*(a2 + ab + b2)

a3 + b3 = (a + b)(a2 - ab + b2) a3 - b3 = (a - b)(a2 + ab + b2)

a3 - b3 = (a - b)(a2 + ab + b2) a3 + b3 = (a + b)(a2 - ab + b2)

(a3 + b3)/(a + b) = (a + b)*(a2 - ab + b2)/(a + b) = (a2 - ab + b2)

(a-b)2 = (a-b)(a-b). You have to multiply each term in the left monomial by each term in the right monomial: a2 - ab - ab + b2 = a2 - 2ab + b2.

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.

Too bad that's not a^2 - ab - 42b^2 That factors to (a + 6b)(a - 7b)

a and b are factors of ab

(a3 + b3) = (a + b)(a2 - ab + b2)