Basic Math Examples

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

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

Step 1

Apply the distributive property.

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

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

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

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

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

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

Step 2.3

Multiply

- 9

$- 9$ by

5

$5$ .

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

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

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply

g

$g$ by

g

$g$ by adding the exponents.

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Step 3.1.1

Move

g

$g$ .

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

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

Step 3.1.2

Multiply

g

$g$ by

g

$g$ .

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

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

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

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

Step 3.2

Multiply

5

$5$ by

3

$3$ .

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

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

Step 3.3

Multiply

g

$g$ by

g^{2}

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

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Step 3.3.1

Move

g^{2}

$g^{2}$ .

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

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

Step 3.3.2

Multiply

g^{2}

$g^{2}$ by

g

$g$ .

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Step 3.3.2.1

Raise

g

$g$ to the power of

1

$1$ .

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

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

Step 3.3.2.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

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

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

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

Step 3.3.3

Add

2

$2$ and

1

$1$ .

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

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

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

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

Step 3.4

Multiply

5

$5$ by

7

$7$ .

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

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

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

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

Step 4

Reorder

15 g^{2}

$15 g^{2}$ and

35 g^{3}

$35 g^{3}$ .

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

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