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} = a^{3} + 3a^{2}b + 3ab^{2} + b^{3} and(a – b)^{3} = a^{3} – 3a^{2}b + 3ab^{2} – b^{3}}

= [ 27r^{3} –{3 × 9r^{2} × 2k } + {3 × 3r × 4k^{2} } – 8k^{3} ] + [ 27r^{3} +{3 × 9r^{2} × 2k } +{3 × 3r ×(4k^{2} } + 8k^{3} ]

= [ 27r^{3} – 54r^{2}k + 36rk^{2} – 8k^{3} ] + [ 27r^{3} + 54r^{2}k + 36rk^{2} + 8k^{3} ]

= 27r^{3} - 54r^{2}k + 36rk^{2} – 8k^{3} + 27r^{3} + 54r^{2}k + 36rk^{2} + 8k^{3}

= 54r^{3} + 72rk^{2}

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