Algebra Examples

$125 x^{3} - 64 y^{3}$

Step 1

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

${(5 x)}^{3} - 64 y^{3}$

Step 2

Rewrite $64 y^{3}$ as ${(4 y)}^{3}$ .

${(5 x)}^{3} - {(4 y)}^{3}$

Step 3

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 $a = 5 x$ and $b = 4 y$ .

$(5 x - (4 y)) ({(5 x)}^{2} + 5 x (4 y) + {(4 y)}^{2})$

Step 4

Simplify.

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Step 4.1

Multiply $4$ by $- 1$ .

$(5 x - 4 y) ({(5 x)}^{2} + 5 x (4 y) + {(4 y)}^{2})$

Step 4.2

Apply the product rule to $5 x$ .

$(5 x - 4 y) (5^{2} x^{2} + 5 x (4 y) + {(4 y)}^{2})$

Step 4.3

Raise $5$ to the power of $2$ .

$(5 x - 4 y) (25 x^{2} + 5 x (4 y) + {(4 y)}^{2})$

Step 4.4

Rewrite using the commutative property of multiplication.

$(5 x - 4 y) (25 x^{2} + 5 \cdot 4 x y + {(4 y)}^{2})$

Step 4.5

Multiply $5$ by $4$ .

$(5 x - 4 y) (25 x^{2} + 20 x y + {(4 y)}^{2})$

Step 4.6

Apply the product rule to $4 y$ .

$(5 x - 4 y) (25 x^{2} + 20 x y + 4^{2} y^{2})$

Step 4.7

Raise $4$ to the power of $2$ .

$(5 x - 4 y) (25 x^{2} + 20 x y + 16 y^{2})$