Simplify $(7 a - 5 b) (49 a^{2} + 35 a b + 25 b^{2})$ .

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Solution

$(7 a - 5 b) (49 a^{2} + 35 a b + 25 b^{2})$

$= (7 a - 5 b) [(7 a)^{2} + 7 a \times 5 b + (5 b)^{2}]$

$= (x - y) (x^{2} + x y + y^{2})$ , where $x = 7 a, y = 5 b$

$= x^{3} - y^{3}$ ............... Using, $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$

$= 343 a^{3} - 125 b^{3}$

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