Algebra Examples

$9 p^{3} q^{4} (3 p^{3} - 5 q)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

Apply the distributive property.

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

Step 3

Multiply $p^{3}$ by $p^{3}$ by adding the exponents.

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Step 3.1

Move $p^{3}$ .

$9 (p^{3} p^{3}) q^{4} \cdot 3 + 9 p^{3} q^{4} (- 5 q)$

Step 3.2

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

$9 p^{3 + 3} q^{4} \cdot 3 + 9 p^{3} q^{4} (- 5 q)$

Step 3.3

Add $3$ and $3$ .

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

Step 4

Multiply $q^{4}$ by $q$ by adding the exponents.

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Step 4.1

Move $q$ .

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

Step 4.2

Multiply $q$ by $q^{4}$ .

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Step 4.2.1

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

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

Step 4.2.2

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

$9 p^{6} q^{4} \cdot 3 + 9 p^{3} q^{1 + 4} \cdot - 5$

Step 4.3

Add $1$ and $4$ .

$9 p^{6} q^{4} \cdot 3 + 9 p^{3} q^{5} \cdot - 5$

Step 5

Simplify each term.

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Step 5.1

Multiply $3$ by $9$ .

$27 p^{6} q^{4} + 9 p^{3} q^{5} \cdot - 5$

Step 5.2

Multiply $- 5$ by $9$ .

$27 p^{6} q^{4} - 45 p^{3} q^{5}$