Trigonometry Examples

$- 8 a^{4} \cdot (16 a^{3}) - 4 a^{2}$

Step 1

Add parentheses.

$- 8 (a^{4} \cdot (16 a^{3})) - 4 a^{2}$

Step 2

Let $u = a^{4} \cdot (16 a^{3})$ . Substitute $u$ for all occurrences of $a^{4} \cdot (16 a^{3})$ .

$- 8 u - 4 a^{2}$

Step 3

Factor $- 4$ out of $- 8 u - 4 a^{2}$ .

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Step 3.1

Reorder $- 8 u$ and $- 4 a^{2}$ .

$- 4 a^{2} - 8 u$

Step 3.2

Factor $- 4$ out of $- 4 a^{2}$ .

$- 4 (a^{2}) - 8 u$

Step 3.3

Factor $- 4$ out of $- 8 u$ .

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

Step 3.4

Factor $- 4$ out of $- 4 (a^{2}) - 4 (2 u)$ .

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

Step 4

Replace all occurrences of $u$ with $a^{4} \cdot (16 a^{3})$ .

$- 4 (a^{2} + 2 (a^{4} \cdot (16 a^{3})))$

Step 5

Simplify each term.

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Step 5.1

Multiply $a^{4}$ by $a^{3}$ by adding the exponents.

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Step 5.1.1

Move $a^{3}$ .

$- 4 (a^{2} + 2 (a^{3} a^{4} \cdot 16))$

Step 5.1.2

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

$- 4 (a^{2} + 2 (a^{3 + 4} \cdot 16))$

Step 5.1.3

Add $3$ and $4$ .

$- 4 (a^{2} + 2 (a^{7} \cdot 16))$

Step 5.2

Move $16$ to the left of $a^{7}$ .

$- 4 (a^{2} + 2 (16 a^{7}))$

Step 5.3

Multiply $16$ by $2$ .

$- 4 (a^{2} + 32 a^{7})$

Step 6

Factor.

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Step 6.1

Factor $a^{2}$ out of $a^{2} + 32 a^{7}$ .

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Step 6.1.1

Multiply by $1$ .

$- 4 (a^{2} \cdot 1 + 32 a^{7})$

Step 6.1.2

Factor $a^{2}$ out of $32 a^{7}$ .

$- 4 (a^{2} \cdot 1 + a^{2} (32 a^{5}))$

Step 6.1.3

Factor $a^{2}$ out of $a^{2} \cdot 1 + a^{2} (32 a^{5})$ .

$- 4 (a^{2} (1 + 32 a^{5}))$

Step 6.2

Remove unnecessary parentheses.

$- 4 a^{2} (1 + 32 a^{5})$