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Question
Simplify.
(3r − 2k)3 + (3r + 2k)3
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Solution
It is known that formula,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
(a − b)3 = a3 − 3a2b + 3ab2 − b3
Given: (3r − 2k)3 + (3r + 2k)3
= (3r)3 − (2k)3 − 3 × (3r)2 × 2k + 3 × 3r × (2k)2 + (3r)3 + (2k)3 + 3 × (3r)2 × 2k + 3 × 3r + (2k)2
= 27 r3 − 8 k3 − 54 rk + 36 rk2 + 27 r3 + 8 k3 + 54 r2k + 36 rk2
= 54 r3 + 72 rk2
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