Q. 2 B4.1( 17 Votes )

Simplify

(3r – 2k)3 +(3r + 2k)3

Answer :

(3r – 2k)3 +(3r + 2k)3 = [(3r)3 -{3 ×(3r)2 ×(2k)} + {3 ×(3r)×(2k)2 } -(2k)3 ] + [(3r)3 +{3 × (3r)2 ×(2k)} + {3 ×(3r)×(2k)2} +(2k)3 ]


{ (a + b)3 = a3 + 3a2b + 3ab2 + b3 and(a – b)3 = a3 – 3a2b + 3ab2 – b3}


= [ 27r3{3 × 9r2 × 2k } + {3 × 3r × 4k2 } – 8k3 ] + [ 27r3 +{3 × 9r2 × 2k } +{3 × 3r ×(4k2 } + 8k3 ]


= [ 27r3 – 54r2k + 36rk2 – 8k3 ] + [ 27r3 + 54r2k + 36rk2 + 8k3 ]


= 27r3 - 54r2k + 36rk2 – 8k3 + 27r3 + 54r2k + 36rk2 + 8k3


= 54r3 + 72rk2


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