Basic Math Examples

$y^{3} - 64 a^{3}$

Step 1

Rewrite

$64 a^{3}$ as

${(4 a)}^{3}$ .

$y^{3} - {(4 a)}^{3}$

Step 2

Since both terms are perfect cubes, factor using the difference of cubes formula,

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

$a = y$ and

$b = 4 a$ .

$(y - (4 a)) (y^{2} + y (4 a) + {(4 a)}^{2})$

Step 3

Simplify.

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Step 3.1

Multiply

$4$ by

$- 1$ .

$(y - 4 a) (y^{2} + y (4 a) + {(4 a)}^{2})$

Step 3.2

Rewrite using the commutative property of multiplication.

$(y - 4 a) (y^{2} + 4 y a + {(4 a)}^{2})$

Step 3.3

Apply the product rule to

$4 a$ .

$(y - 4 a) (y^{2} + 4 y a + 4^{2} a^{2})$

Step 3.4

Raise

$4$ to the power of

$2$ .

$(y - 4 a) (y^{2} + 4 y a + 16 a^{2})$