Pre-Algebra Examples

$216 x^{9} + 125 y^{3}$

Step 1

Rewrite $216 x^{9}$ as ${(6 x^{3})}^{3}$ .

${(6 x^{3})}^{3} + 125 y^{3}$

Step 2

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

${(6 x^{3})}^{3} + {(5 y)}^{3}$

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 $a = 6 x^{3}$ and $b = 5 y$ .

$(6 x^{3} + 5 y) ({(6 x^{3})}^{2} - (6 x^{3}) (5 y) + {(5 y)}^{2})$

Step 4

Simplify.

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Step 4.1

Apply the product rule to $6 x^{3}$ .

$(6 x^{3} + 5 y) (6^{2} {(x^{3})}^{2} - (6 x^{3}) (5 y) + {(5 y)}^{2})$

Step 4.2

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

$(6 x^{3} + 5 y) (36 {(x^{3})}^{2} - (6 x^{3}) (5 y) + {(5 y)}^{2})$

Step 4.3

Multiply the exponents in ${(x^{3})}^{2}$ .

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Step 4.3.1

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

$(6 x^{3} + 5 y) (36 x^{3 \cdot 2} - (6 x^{3}) (5 y) + {(5 y)}^{2})$

Step 4.3.2

Multiply $3$ by $2$ .

$(6 x^{3} + 5 y) (36 x^{6} - (6 x^{3}) (5 y) + {(5 y)}^{2})$

Step 4.4

Multiply $6$ by $- 1$ .

$(6 x^{3} + 5 y) (36 x^{6} - 6 x^{3} (5 y) + {(5 y)}^{2})$

Step 4.5

Rewrite using the commutative property of multiplication.

$(6 x^{3} + 5 y) (36 x^{6} - 6 \cdot 5 x^{3} y + {(5 y)}^{2})$

Step 4.6

Multiply $- 6$ by $5$ .

$(6 x^{3} + 5 y) (36 x^{6} - 30 x^{3} y + {(5 y)}^{2})$

Step 4.7

Apply the product rule to $5 y$ .

$(6 x^{3} + 5 y) (36 x^{6} - 30 x^{3} y + 5^{2} y^{2})$

Step 4.8

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

$(6 x^{3} + 5 y) (36 x^{6} - 30 x^{3} y + 25 y^{2})$