Factor 8c^3-125d^3 - MathMaster

$8 c^{3} - 125 d^{3}$

Rewrite $8 c^{3}$ as ${(2 c)}^{3}$ .

${(2 c)}^{3} - 125 d^{3}$

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

${(2 c)}^{3} - {(5 d)}^{3}$

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 $a = 2 c$ and $b = 5 d$ .

$(2 c - (5 d)) ({(2 c)}^{2} + 2 c (5 d) + {(5 d)}^{2})$

Simplify.

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Multiply $5$ by $- 1$ .

$(2 c - 5 d) ({(2 c)}^{2} + 2 c (5 d) + {(5 d)}^{2})$

Apply the product rule to $2 c$ .

$(2 c - 5 d) (2^{2} c^{2} + 2 c (5 d) + {(5 d)}^{2})$

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

$(2 c - 5 d) (4 c^{2} + 2 c (5 d) + {(5 d)}^{2})$

Rewrite using the commutative property of multiplication.

$(2 c - 5 d) (4 c^{2} + 2 \cdot 5 c d + {(5 d)}^{2})$

Multiply $2$ by $5$ .

$(2 c - 5 d) (4 c^{2} + 10 c d + {(5 d)}^{2})$

Apply the product rule to $5 d$ .

$(2 c - 5 d) (4 c^{2} + 10 c d + 5^{2} d^{2})$

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

$(2 c - 5 d) (4 c^{2} + 10 c d + 25 d^{2})$

Factor 8c^3-125d^3

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