Basic Math Examples

$125 R^{6} + 216 G^{3}$

Step 1

Rewrite $125 R^{6}$ as ${(5 R^{2})}^{3}$ .

${(5 R^{2})}^{3} + 216 G^{3}$

Step 2

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

${(5 R^{2})}^{3} + {(6 G)}^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula, $a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where $a = 5 R^{2}$ and $b = 6 G$ .

$(5 R^{2} + 6 G) ({(5 R^{2})}^{2} - (5 R^{2}) (6 G) + {(6 G)}^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $5 R^{2}$ .

$(5 R^{2} + 6 G) (5^{2} {(R^{2})}^{2} - (5 R^{2}) (6 G) + {(6 G)}^{2})$

Step 4.2

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

$(5 R^{2} + 6 G) (25 {(R^{2})}^{2} - (5 R^{2}) (6 G) + {(6 G)}^{2})$

Step 4.3

Multiply the exponents in ${(R^{2})}^{2}$ .

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Step 4.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$(5 R^{2} + 6 G) (25 R^{2 \cdot 2} - (5 R^{2}) (6 G) + {(6 G)}^{2})$

Step 4.3.2

Multiply $2$ by $2$ .

$(5 R^{2} + 6 G) (25 R^{4} - (5 R^{2}) (6 G) + {(6 G)}^{2})$

Step 4.4

Multiply $5$ by $- 1$ .

$(5 R^{2} + 6 G) (25 R^{4} - 5 R^{2} (6 G) + {(6 G)}^{2})$

Step 4.5

Rewrite using the commutative property of multiplication.

$(5 R^{2} + 6 G) (25 R^{4} - 5 \cdot 6 R^{2} G + {(6 G)}^{2})$

Step 4.6

Multiply $- 5$ by $6$ .

$(5 R^{2} + 6 G) (25 R^{4} - 30 R^{2} G + {(6 G)}^{2})$

Step 4.7

Apply the product rule to $6 G$ .

$(5 R^{2} + 6 G) (25 R^{4} - 30 R^{2} G + 6^{2} G^{2})$

Step 4.8

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

$(5 R^{2} + 6 G) (25 R^{4} - 30 R^{2} G + 36 G^{2})$