Algebra Examples

$- 3 g (7 g - 2) + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$- 3 g (7 g) - 3 g \cdot - 2 + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.2

Rewrite using the commutative property of multiplication.

$- 3 \cdot 7 g \cdot g - 3 g \cdot - 2 + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.3

Multiply $- 2$ by $- 3$ .

$- 3 \cdot 7 g \cdot g + 6 g + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

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Step 1.4.1.1

Move $g$ .

$- 3 \cdot 7 (g \cdot g) + 6 g + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.4.1.2

Multiply $g$ by $g$ .

$- 3 \cdot 7 g^{2} + 6 g + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.4.2

Multiply $- 3$ by $7$ .

$- 21 g^{2} + 6 g + 3 (g^{2} + 2 g + 1) - 3 g (- 5 g + 3)$

Step 1.5

Apply the distributive property.

$- 21 g^{2} + 6 g + 3 g^{2} + 3 (2 g) + 3 \cdot 1 - 3 g (- 5 g + 3)$

Step 1.6

Simplify.

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Step 1.6.1

Multiply $2$ by $3$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 \cdot 1 - 3 g (- 5 g + 3)$

Step 1.6.2

Multiply $3$ by $1$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 g (- 5 g + 3)$

Step 1.7

Apply the distributive property.

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 g (- 5 g) - 3 g \cdot 3$

Step 1.8

Rewrite using the commutative property of multiplication.

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 \cdot - 5 g \cdot g - 3 g \cdot 3$

Step 1.9

Multiply $3$ by $- 3$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 \cdot - 5 g \cdot g - 9 g$

Step 1.10

Simplify each term.

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Step 1.10.1

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

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Step 1.10.1.1

Move $g$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 \cdot - 5 (g \cdot g) - 9 g$

Step 1.10.1.2

Multiply $g$ by $g$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 - 3 \cdot - 5 g^{2} - 9 g$

Step 1.10.2

Multiply $- 3$ by $- 5$ .

$- 21 g^{2} + 6 g + 3 g^{2} + 6 g + 3 + 15 g^{2} - 9 g$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 21 g^{2}$ and $3 g^{2}$ .

$- 18 g^{2} + 6 g + 6 g + 3 + 15 g^{2} - 9 g$

Step 2.2

Add $- 18 g^{2}$ and $15 g^{2}$ .

$- 3 g^{2} + 6 g + 6 g + 3 - 9 g$

Step 2.3

Add $6 g$ and $6 g$ .

$- 3 g^{2} + 12 g + 3 - 9 g$

Step 2.4

Subtract $9 g$ from $12 g$ .

$- 3 g^{2} + 3 g + 3$