(96)^3 = (100 4)^3 = #160; ^3C_0 (100)^3 #160;^3C_1 (100)^2(4) + #160;^3C_2 (100)(4)^2 #160;^3C_3 (4)^3 = (100)^3 3(100)^2 (4) + 3( ...

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Formation of Algebraic Expressions

Evaluate 96...

Question

Evaluate $(96)^{3}$

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Solution

$(96)^{3} = (100 - 4)^{3}$
$=^{3} C_{0} (100)^{3} -^{3} C_{1} (100)^{2} (4) +^{3} C_{2} (100) (4)^{2} -^{3} C_{3} (4)^{3}$
$= (100)^{3} - 3 (100)^{2} (4) + 3 (100) (4)^{2} - (4)^{3}$
$= 1000000 - 120000 + 4800 - 64$
$= 884736$

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