Basic Math Examples

$5 g (3 g + 7 g^{2} - 9)$

Step 1

Apply the distributive property.

$5 g (3 g) + 5 g (7 g^{2}) + 5 g \cdot - 9$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$5 \cdot 3 g \cdot g + 5 g (7 g^{2}) + 5 g \cdot - 9$

Step 2.2

Rewrite using the commutative property of multiplication.

$5 \cdot 3 g \cdot g + 5 \cdot 7 g \cdot g^{2} + 5 g \cdot - 9$

Step 2.3

Multiply $- 9$ by $5$ .

$5 \cdot 3 g \cdot g + 5 \cdot 7 g \cdot g^{2} - 45 g$

Step 3

Simplify each term.

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Step 3.1

Multiply $g$ by $g$ by adding the exponents.

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Step 3.1.1

Move $g$ .

$5 \cdot 3 (g \cdot g) + 5 \cdot 7 g \cdot g^{2} - 45 g$

Step 3.1.2

Multiply $g$ by $g$ .

$5 \cdot 3 g^{2} + 5 \cdot 7 g \cdot g^{2} - 45 g$

Step 3.2

Multiply $5$ by $3$ .

$15 g^{2} + 5 \cdot 7 g \cdot g^{2} - 45 g$

Step 3.3

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

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Step 3.3.1

Move $g^{2}$ .

$15 g^{2} + 5 \cdot 7 (g^{2} g) - 45 g$

Step 3.3.2

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

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Step 3.3.2.1

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

$15 g^{2} + 5 \cdot 7 (g^{2} g^{1}) - 45 g$

Step 3.3.2.2

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

$15 g^{2} + 5 \cdot 7 g^{2 + 1} - 45 g$

Step 3.3.3

Add $2$ and $1$ .

$15 g^{2} + 5 \cdot 7 g^{3} - 45 g$

Step 3.4

Multiply $5$ by $7$ .

$15 g^{2} + 35 g^{3} - 45 g$

Step 4

Reorder $15 g^{2}$ and $35 g^{3}$ .

$35 g^{3} + 15 g^{2} - 45 g$