Simplify: a-ba23+ab3+b23-a+ba23-ab3+b23
Explanation:
x3 – y3 = (x - y)(x2 + xy + y2) x3 + y3 = (x + y)(x2 - xy + y2)
Consider, a – b
It can be written as (∛a)3 - (∛b)3
∴ a – b = (∛a)3 - (∛b)3 = (∛a - ∛b)((∛a)2 + ∛a × ∛b + (∛b)2)
Similarly,
∴ a + b = (∛a)3 + (∛b)3 = (∛a + ∛b)((∛a)2 - ∛a × ∛b + (∛b)2)
We need to find,
a-ba23+ab3+b23 - a+ba23-ab3+b23
= a3 - b3a32 + ab3 + b32a23+ab3+b23 - a3+ b3a32- ab3 + b32a23-ab3+b23
= (∛a - ∛b) – (∛a + ∛b)
= -2 × ∛b
Hence, option (c).
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