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Expansion of (a ± b)³

Evaluate the ...

Question

Evaluate the following:

(iii) $104^{3} + 96^{3}$

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Solution

Given, $104^{3} + 96^{3}$

Using Identity,

$(a + b)^{3} = a^{3} + b^{3} + 3 a b (a + b)$

$∴ a^{3} + b^{3} = (a + b)^{3} - 3 a b (a + b)$

$∴ 104^{3} + 96^{3}$

$= (104 + 96)^{3} - 3 \times 104 \times 96 (104 + 96)$

$= (200)^{3} - 3 \times 104 \times 96 (200)$

$= 8000000 - 29952 (200)$

$= 8000000 - 5990400$

$= 2009600$

$∴ 104^{3} + 96^{3} = 2009600$

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Expansion of (a ± b)³

Standard IX Mathematics

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