Trigonometry Examples

$(5 q^{5} + 4) - (2 q^{3} + 9) (6 q^{5} - 9^{3})$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 q^{5} + 4 + (- (2 q^{3}) - 1 \cdot 9) (6 q^{5} - 9^{3})$

Step 1.2

Multiply $2$ by $- 1$ .

$5 q^{5} + 4 + (- 2 q^{3} - 1 \cdot 9) (6 q^{5} - 9^{3})$

Step 1.3

Multiply $- 1$ by $9$ .

$5 q^{5} + 4 + (- 2 q^{3} - 9) (6 q^{5} - 9^{3})$

Step 1.4

Simplify each term.

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Step 1.4.1

Raise $9$ to the power of $3$ .

$5 q^{5} + 4 + (- 2 q^{3} - 9) (6 q^{5} - 1 \cdot 729)$

Step 1.4.2

Multiply $- 1$ by $729$ .

$5 q^{5} + 4 + (- 2 q^{3} - 9) (6 q^{5} - 729)$

Step 1.5

Expand $(- 2 q^{3} - 9) (6 q^{5} - 729)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$5 q^{5} + 4 - 2 q^{3} (6 q^{5} - 729) - 9 (6 q^{5} - 729)$

Step 1.5.2

Apply the distributive property.

$5 q^{5} + 4 - 2 q^{3} (6 q^{5}) - 2 q^{3} \cdot - 729 - 9 (6 q^{5} - 729)$

Step 1.5.3

Apply the distributive property.

$5 q^{5} + 4 - 2 q^{3} (6 q^{5}) - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6

Simplify each term.

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Step 1.6.1

Rewrite using the commutative property of multiplication.

$5 q^{5} + 4 - 2 \cdot 6 q^{3} q^{5} - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.2

Multiply $q^{3}$ by $q^{5}$ by adding the exponents.

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Step 1.6.2.1

Move $q^{5}$ .

$5 q^{5} + 4 - 2 \cdot 6 (q^{5} q^{3}) - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.2.2

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

$5 q^{5} + 4 - 2 \cdot 6 q^{5 + 3} - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.2.3

Add $5$ and $3$ .

$5 q^{5} + 4 - 2 \cdot 6 q^{8} - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.3

Multiply $- 2$ by $6$ .

$5 q^{5} + 4 - 12 q^{8} - 2 q^{3} \cdot - 729 - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.4

Multiply $- 729$ by $- 2$ .

$5 q^{5} + 4 - 12 q^{8} + 1458 q^{3} - 9 (6 q^{5}) - 9 \cdot - 729$

Step 1.6.5

Multiply $6$ by $- 9$ .

$5 q^{5} + 4 - 12 q^{8} + 1458 q^{3} - 54 q^{5} - 9 \cdot - 729$

Step 1.6.6

Multiply $- 9$ by $- 729$ .

$5 q^{5} + 4 - 12 q^{8} + 1458 q^{3} - 54 q^{5} + 6561$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $54 q^{5}$ from $5 q^{5}$ .

$- 49 q^{5} + 4 - 12 q^{8} + 1458 q^{3} + 6561$

Step 2.2

Add $4$ and $6561$ .

$- 49 q^{5} - 12 q^{8} + 1458 q^{3} + 6565$