Basic Math Examples

$64 - a^{6}$

Step 1

Rewrite $64$ as $4^{3}$ .

$4^{3} - a^{6}$

Step 2

Rewrite $a^{6}$ as ${(a^{2})}^{3}$ .

$4^{3} - {(a^{2})}^{3}$

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 $a = 4$ and $b = a^{2}$ .

$(4 - a^{2}) (4^{2} + 4 a^{2} + {(a^{2})}^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Rewrite $4$ as $2^{2}$ .

$(2^{2} - a^{2}) (4^{2} + 4 a^{2} + {(a^{2})}^{2})$

Step 4.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2$ and $b = a$ .

$(2 + a) (2 - a) (4^{2} + 4 a^{2} + {(a^{2})}^{2})$

Step 4.3

Raise $4$ to the power of $2$ .

$(2 + a) (2 - a) (16 + 4 a^{2} + {(a^{2})}^{2})$

Step 4.4

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

Tap for more steps...

Step 4.4.1

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

$(2 + a) (2 - a) (16 + 4 a^{2} + a^{2 \cdot 2})$

Step 4.4.2

Multiply $2$ by $2$ .

$(2 + a) (2 - a) (16 + 4 a^{2} + a^{4})$

Step 4.5

Factor.

Tap for more steps...

Step 4.5.1

Rewrite $16 + 4 a^{2} + a^{4}$ in a factored form.

Tap for more steps...

Step 4.5.1.1

Rewrite the middle term.

$(2 + a) (2 - a) (16 + 2 \cdot 4 a^{2} - 4 a^{2} + a^{4})$

Step 4.5.1.2

Rearrange terms.

$(2 + a) (2 - a) (16 + 2 \cdot 4 a^{2} + a^{4} - 4 a^{2})$

Step 4.5.1.3

Factor first three terms by perfect square rule.

$(2 + a) (2 - a) ({(4 + a^{2})}^{2} - 4 a^{2})$

Step 4.5.1.4

Rewrite $4 a^{2}$ as ${(2 a)}^{2}$ .

$(2 + a) (2 - a) ({(4 + a^{2})}^{2} - {(2 a)}^{2})$

Step 4.5.1.5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4 + a^{2}$ and $b = 2 a$ .

$(2 + a) (2 - a) ((4 + a^{2} + 2 a) (4 + a^{2} - (2 a)))$

Step 4.5.1.6

Simplify.

Tap for more steps...

Step 4.5.1.6.1

Reorder terms.

$(2 + a) (2 - a) ((a^{2} + 2 a + 4) (4 + a^{2} - (2 a)))$

Step 4.5.1.6.2

Multiply $2$ by $- 1$ .

$(2 + a) (2 - a) ((a^{2} + 2 a + 4) (4 + a^{2} - 2 a))$

Step 4.5.1.6.3

Reorder terms.

$(2 + a) (2 - a) ((a^{2} + 2 a + 4) (a^{2} - 2 a + 4))$

Step 4.5.2

Remove unnecessary parentheses.

$(2 + a) (2 - a) (a^{2} + 2 a + 4) (a^{2} - 2 a + 4)$