Basic Math Examples

$d^{2} \cdot (4 d) - 32$

Step 1

Factor $4$ out of $d^{2} \cdot (4 d) - 32$ .

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Step 1.1

Factor $4$ out of $d^{2} \cdot (4 d)$ .

$4 (d^{2} \cdot (d)) - 32$

Step 1.2

Factor $4$ out of $- 32$ .

$4 (d^{2} \cdot (d)) + 4 \cdot - 8$

Step 1.3

Factor $4$ out of $4 (d^{2} \cdot (d)) + 4 \cdot - 8$ .

$4 (d^{2} \cdot (d) - 8)$

Step 2

Multiply $d^{2}$ by $d$ by adding the exponents.

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Step 2.1

Multiply $d^{2}$ by $d$ .

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Step 2.1.1

Raise $d$ to the power of $1$ .

$4 (d^{2} \cdot d^{1} - 8)$

Step 2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 (d^{2 + 1} - 8)$

Step 2.2

Add $2$ and $1$ .

$4 (d^{3} - 8)$

Step 3

Rewrite $8$ as $2^{3}$ .

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

Step 4

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 $a = d$ and $b = 2$ .

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

Step 5

Factor.

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Step 5.1

Simplify.

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Step 5.1.1

Move $2$ to the left of $d$ .

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

Step 5.1.2

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

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

Step 5.2

Remove unnecessary parentheses.

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