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Multiplication of Monomials

If a - b = ...

Question

If $a - b = 7, a^{2} + b^{2} = 85,$ , find $a^{3} - b^{3}$ .

453

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460

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469

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475

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Solution

The correct option is C $469$
Given, $a - b = 7, a^{2} + b^{2} = 85$

$a^{3} - b^{3} = (a - b) (a^{2} + b^{2} - a b)$ .......(1)

$(a - b)^{2} = a^{2} + b^{2} - 2 a b$

$49 = 85 - 2 a b ⟹ a b = 18$

From eqn (1)

$a^{3} - b^{3} = 7 (85 - 18)$

$= 7 \times 67 = 469$

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