Factorize the expression $7 x^{3} + 56 y^{3}$ .

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Solution

Factorizing the given expression:
The given expression is $7 x^{3} + 56 y^{3}$ .
By taking $7$ common :
$7 x^{3} + 56 y^{3} = 7 (x^{3} + 8 y^{3}) = 7 [x^{3} + {(2 y)}^{3}] . . . . . . (1)$
We know identity, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ .
Comparing equation (1) with identity we get, $a = x, b = 2 y$ .
Substituting values in the identity we get:
$7 [x^{3} + {(2 y)}^{3}] = 7 (x + 2 y) [x^{2} - (2 y) x + {(2 y)}^{2}] = 7 (x + 2 y) (x^{2} - 2 x y + 4 y^{2})$
Thus, the expression, $7 x^{3} + 56 y^{3} = 7 (x + 2 y) (x^{2} - 2 x y + 4 y^{2})$ .

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