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Factorisation by Common Factors

Solve: 343a...

Question

Solve: $343 a^{3} - b^{3} - 147 a^{2} b + 21 a b^{2}$

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Solution

$343 a^{3} - b^{3} - 147 a^{2} b + 21 a b^{2}$
$\Rightarrow$ Using ${(a - b)}^{3} = a^{3} - b^{3} - 3 a^{2} b + 3 a b^{2}$
$= {(7 a)}^{3} - {(b)}^{3} - 3 {(7 a)}^{2} b + 3 (7 a) {(b)}^{2}$
$= {(7 a - b)}^{3}$
Hence, the answer is ${(7 a - b)}^{3} .$

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