Algebra Examples

$g^{2} + \frac{1}{4} (44 g^{2} - 12 g + 8) - 8 g$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$g^{2} + \frac{1}{4} (44 g^{2}) + \frac{1}{4} (- 12 g) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2

Simplify.

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Step 1.2.1

Cancel the common factor of $4$ .

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Step 1.2.1.1

Factor $4$ out of $44 g^{2}$ .

$g^{2} + \frac{1}{4} (4 (11 g^{2})) + \frac{1}{4} (- 12 g) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.1.2

Cancel the common factor.

$g^{2} + \frac{1}{4} (4 (11 g^{2})) + \frac{1}{4} (- 12 g) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.1.3

Rewrite the expression.

$g^{2} + 11 g^{2} + \frac{1}{4} (- 12 g) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.2

Cancel the common factor of $4$ .

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Step 1.2.2.1

Factor $4$ out of $- 12 g$ .

$g^{2} + 11 g^{2} + \frac{1}{4} (4 (- 3 g)) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.2.2

Cancel the common factor.

$g^{2} + 11 g^{2} + \frac{1}{4} (4 (- 3 g)) + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.2.3

Rewrite the expression.

$g^{2} + 11 g^{2} - 3 g + \frac{1}{4} \cdot 8 - 8 g$

Step 1.2.3

Cancel the common factor of $4$ .

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Step 1.2.3.1

Factor $4$ out of $8$ .

$g^{2} + 11 g^{2} - 3 g + \frac{1}{4} \cdot (4 (2)) - 8 g$

Step 1.2.3.2

Cancel the common factor.

$g^{2} + 11 g^{2} - 3 g + \frac{1}{4} \cdot (4 \cdot 2) - 8 g$

Step 1.2.3.3

Rewrite the expression.

$g^{2} + 11 g^{2} - 3 g + 2 - 8 g$

Step 2

Simplify by adding terms.

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Step 2.1

Add $g^{2}$ and $11 g^{2}$ .

$12 g^{2} - 3 g + 2 - 8 g$

Step 2.2

Subtract $8 g$ from $- 3 g$ .

$12 g^{2} - 11 g + 2$