Simplify
(2a + b)3 –(2a – b)3
(2a + b)3 –(2a – b)3 = [(2a)3 +{3 ×(2a)2 × b } + {3 ×(2a)×(b)2 } +(b)3 ] - [(2a)3 -{3 × (2a)2 × b } +{3 ×(2a)×(b)2 } -(b)3 ]
{ ∵(a + b)3 = a3 + 3a2b + 3ab2 + b3 and(a – b)3 = a3 – 3a2b + 3ab2 – b3 }
= [ 8a3 +{3 × 4a2× b } +{3 × 2a ×b } + b3 ] – [ 8a3 – { 3 × 4a2× b } +{3 × 2a × b2 } – b3 ]
= [ 8a3 + 12a2b + 6ab2 + b3 ] – [ 8a3 – 12a2b + 6ab2 – b3 ]
= 8a3 + 12a2b + 6ab2 + b3 – 8a3 + 12a2b – 6ab2 + b3
= 24a2b + 2b3
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Generated by AI. May contain inaccuracies — always verify with your textbook.
