Factorize the expression $x^{3} - 64 y^{3}$ .

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Solution

Factorizing the given expression:
The given expression is $x^{3} - 64 y^{3}$ .
$x^{3} - 64 y^{3} = x^{3} - {(4 y)}^{3}$
Use identity $a^{3} - b^{3} = (a - b) (a^{2} + a b + b^{2})$ to expand.
Here, $a = x, b = 4 y$ .
$x^{3} - {(4 y)}^{3} = (x - 4 y) [x^{2} - x (4 y) + {(4 y)}^{2}] = (x - 4 y) (x^{2} - 4 x y + 16 y^{2})$
Therefore, the expression, $x^{3} - 64 y^{3} = (x - 4 y) (x^{2} - 4 x y + 16 y^{2})$ .

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Factorize the expression x3-64y3.

Factorizing the given expression:The given expression is x3-64y3.x3-64y3=x3-4y3Use identity a3-b3=(a-b)a2+ab+b2 to expand.Here, a=x,b=4y.x3-4y3=x-4yx2-x4y+4y2=x-4yx2-4xy+16y2Therefore, the expression, x3-64y3=x-4yx2-4xy+16y2.

Factorize the expression $x^{3} - 64 y^{3}$ .