Trigonometry Examples

$8 a^{5} (9 a - 5) - (9 a - 5)$

Step 1

Apply the distributive property.

$8 a^{5} (9 a) + 8 a^{5} \cdot - 5 - (9 a - 5)$

Step 2

Rewrite using the commutative property of multiplication.

$8 \cdot 9 a^{5} a + 8 a^{5} \cdot - 5 - (9 a - 5)$

Step 3

Multiply $- 5$ by $8$ .

$8 \cdot 9 a^{5} a - 40 a^{5} - (9 a - 5)$

Step 4

Simplify each term.

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Step 4.1

Multiply $a^{5}$ by $a$ by adding the exponents.

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Step 4.1.1

Move $a$ .

$8 \cdot 9 (a \cdot a^{5}) - 40 a^{5} - (9 a - 5)$

Step 4.1.2

Multiply $a$ by $a^{5}$ .

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Step 4.1.2.1

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

$8 \cdot 9 (a^{1} a^{5}) - 40 a^{5} - (9 a - 5)$

Step 4.1.2.2

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

$8 \cdot 9 a^{1 + 5} - 40 a^{5} - (9 a - 5)$

Step 4.1.3

Add $1$ and $5$ .

$8 \cdot 9 a^{6} - 40 a^{5} - (9 a - 5)$

Step 4.2

Multiply $8$ by $9$ .

$72 a^{6} - 40 a^{5} - (9 a - 5)$

Step 5

Apply the distributive property.

$72 a^{6} - 40 a^{5} - (9 a) - - 5$

Step 6

Multiply $9$ by $- 1$ .

$72 a^{6} - 40 a^{5} - 9 a - - 5$

Step 7

Multiply $- 1$ by $- 5$ .

$72 a^{6} - 40 a^{5} - 9 a + 5$