Basic Math Examples

$1 + 343 a^{3} b^{9}$

Step 1

Rewrite $1$ as $1^{3}$ .

$1^{3} + 343 a^{3} b^{9}$

Step 2

Rewrite $343 a^{3} b^{9}$ as ${(7 a b^{3})}^{3}$ .

$1^{3} + {(7 a b^{3})}^{3}$

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 $a = 1$ and $b = 7 a b^{3}$ .

$(1 + 7 a b^{3}) (1^{2} - 1 (7 a b^{3}) + {(7 a b^{3})}^{2})$

Step 4

Simplify.

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Step 4.1

One to any power is one.

$(1 + 7 a b^{3}) (1 - 1 (7 a b^{3}) + {(7 a b^{3})}^{2})$

Step 4.2

Multiply $7$ by $- 1$ .

$(1 + 7 a b^{3}) (1 - 7 (a b^{3}) + {(7 a b^{3})}^{2})$

Step 4.3

Remove parentheses.

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + {(7 a b^{3})}^{2})$

Step 4.4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.4.1

Apply the product rule to $7 a b^{3}$ .

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + {(7 a)}^{2} {(b^{3})}^{2})$

Step 4.4.2

Apply the product rule to $7 a$ .

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + 7^{2} a^{2} {(b^{3})}^{2})$

Step 4.5

Raise $7$ to the power of $2$ .

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + 49 a^{2} {(b^{3})}^{2})$

Step 4.6

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

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Step 4.6.1

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

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + 49 a^{2} b^{3 \cdot 2})$

Step 4.6.2

Multiply $3$ by $2$ .

$(1 + 7 a b^{3}) (1 - 7 a b^{3} + 49 a^{2} b^{6})$