Basic Math Examples

$125 m^{3} - 216 r^{3}$

Step 1

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

${(5 m)}^{3} - 216 r^{3}$

Step 2

Rewrite $216 r^{3}$ as ${(6 r)}^{3}$ .

${(5 m)}^{3} - {(6 r)}^{3}$

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 $a = 5 m$ and $b = 6 r$ .

$(5 m - (6 r)) ({(5 m)}^{2} + 5 m (6 r) + {(6 r)}^{2})$

Step 4

Simplify.

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Step 4.1

Multiply $6$ by $- 1$ .

$(5 m - 6 r) ({(5 m)}^{2} + 5 m (6 r) + {(6 r)}^{2})$

Step 4.2

Apply the product rule to $5 m$ .

$(5 m - 6 r) (5^{2} m^{2} + 5 m (6 r) + {(6 r)}^{2})$

Step 4.3

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

$(5 m - 6 r) (25 m^{2} + 5 m (6 r) + {(6 r)}^{2})$

Step 4.4

Rewrite using the commutative property of multiplication.

$(5 m - 6 r) (25 m^{2} + 5 \cdot 6 m r + {(6 r)}^{2})$

Step 4.5

Multiply $5$ by $6$ .

$(5 m - 6 r) (25 m^{2} + 30 m r + {(6 r)}^{2})$

Step 4.6

Apply the product rule to $6 r$ .

$(5 m - 6 r) (25 m^{2} + 30 m r + 6^{2} r^{2})$

Step 4.7

Raise $6$ to the power of $2$ .

$(5 m - 6 r) (25 m^{2} + 30 m r + 36 r^{2})$