Algebra Examples

$\frac{1}{2} x - (- 2 x + \frac{1}{10} (3 x^{2} - 5 (\frac{1}{4} x - x^{2}) + \frac{1}{4} x^{2}))$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} - 5 (\frac{1}{4} x - x^{2}) + \frac{1}{4} x^{2}))$

Step 1.2

Simplify each term.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} - 5 (\frac{x}{4} - x^{2}) + \frac{1}{4} x^{2}))$

Step 1.2.1.2

Apply the distributive property.

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} - 5 \frac{x}{4} - 5 (- x^{2}) + \frac{1}{4} x^{2}))$

Step 1.2.1.3

Combine $- 5$ and $\frac{x}{4}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} + \frac{- 5 x}{4} - 5 (- x^{2}) + \frac{1}{4} x^{2}))$

Step 1.2.1.4

Multiply $- 1$ by $- 5$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} + \frac{- 5 x}{4} + 5 x^{2} + \frac{1}{4} x^{2}))$

Step 1.2.1.5

Move the negative in front of the fraction.

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} - \frac{5 x}{4} + 5 x^{2} + \frac{1}{4} x^{2}))$

Step 1.2.1.6

Combine $\frac{1}{4}$ and $x^{2}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (3 x^{2} - \frac{5 x}{4} + 5 x^{2} + \frac{x^{2}}{4}))$

Step 1.2.2

Add $3 x^{2}$ and $5 x^{2}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (8 x^{2} - \frac{5 x}{4} + \frac{x^{2}}{4}))$

Step 1.2.3

To write $8 x^{2}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (- \frac{5 x}{4} + 8 x^{2} \cdot \frac{4}{4} + \frac{x^{2}}{4}))$

Step 1.2.4

Combine $8 x^{2}$ and $\frac{4}{4}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (- \frac{5 x}{4} + \frac{8 x^{2} \cdot 4}{4} + \frac{x^{2}}{4}))$

Step 1.2.5

Combine the numerators over the common denominator.

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot (- \frac{5 x}{4} + \frac{8 x^{2} \cdot 4 + x^{2}}{4}))$

Step 1.2.6

Combine the numerators over the common denominator.

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{- 5 x + 8 x^{2} \cdot 4 + x^{2}}{4})$

Step 1.2.7

Multiply $4$ by $8$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{- 5 x + 32 x^{2} + x^{2}}{4})$

Step 1.2.8

Add $32 x^{2}$ and $x^{2}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{- 5 x + 33 x^{2}}{4})$

Step 1.2.9

Factor $x$ out of $- 5 x + 33 x^{2}$ .

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Step 1.2.9.1

Factor $x$ out of $- 5 x$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{x \cdot - 5 + 33 x^{2}}{4})$

Step 1.2.9.2

Factor $x$ out of $33 x^{2}$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{x \cdot - 5 + x (33 x)}{4})$

Step 1.2.9.3

Factor $x$ out of $x \cdot - 5 + x (33 x)$ .

$\frac{x}{2} - (- 2 x + \frac{1}{10} \cdot \frac{x (- 5 + 33 x)}{4})$

Step 1.2.10

Multiply $\frac{1}{10} \cdot \frac{x (- 5 + 33 x)}{4}$ .

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Step 1.2.10.1

Multiply $\frac{1}{10}$ by $\frac{x (- 5 + 33 x)}{4}$ .

$\frac{x}{2} - (- 2 x + \frac{x (- 5 + 33 x)}{10 \cdot 4})$

Step 1.2.10.2

Multiply $10$ by $4$ .

$\frac{x}{2} - (- 2 x + \frac{x (- 5 + 33 x)}{40})$

Step 1.3

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{40}{40}$ .

$\frac{x}{2} - (- 2 x \cdot \frac{40}{40} + \frac{x (- 5 + 33 x)}{40})$

Step 1.4

Combine $- 2 x$ and $\frac{40}{40}$ .

$\frac{x}{2} - (\frac{- 2 x \cdot 40}{40} + \frac{x (- 5 + 33 x)}{40})$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x}{2} - \frac{- 2 x \cdot 40 + x (- 5 + 33 x)}{40}$

Step 1.6

Simplify the numerator.

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Step 1.6.1

Factor $x$ out of $- 2 x \cdot 40 + x (- 5 + 33 x)$ .

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Step 1.6.1.1

Factor $x$ out of $- 2 x \cdot 40$ .

$\frac{x}{2} - \frac{x (- 2 \cdot 40) + x (- 5 + 33 x)}{40}$

Step 1.6.1.2

Factor $x$ out of $x (- 2 \cdot 40) + x (- 5 + 33 x)$ .

$\frac{x}{2} - \frac{x (- 2 \cdot 40 - 5 + 33 x)}{40}$

Step 1.6.2

Multiply $- 2$ by $40$ .

$\frac{x}{2} - \frac{x (- 80 - 5 + 33 x)}{40}$

Step 1.6.3

Subtract $5$ from $- 80$ .

$\frac{x}{2} - \frac{x (- 85 + 33 x)}{40}$

Step 2

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{20}{20}$ .

$\frac{x}{2} \cdot \frac{20}{20} - \frac{x (- 85 + 33 x)}{40}$

Step 3

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x}{2}$ by $\frac{20}{20}$ .

$\frac{x \cdot 20}{2 \cdot 20} - \frac{x (- 85 + 33 x)}{40}$

Step 3.2

Multiply $2$ by $20$ .

$\frac{x \cdot 20}{40} - \frac{x (- 85 + 33 x)}{40}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot 20 - x (- 85 + 33 x)}{40}$

Step 5

Simplify the numerator.

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Step 5.1

Factor $x$ out of $x \cdot 20 - x (- 85 + 33 x)$ .

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Step 5.1.1

Factor $x$ out of $x \cdot 20$ .

$\frac{x (20) - x (- 85 + 33 x)}{40}$

Step 5.1.2

Factor $x$ out of $- x (- 85 + 33 x)$ .

$\frac{x (20) + x (- (- 85 + 33 x))}{40}$

Step 5.1.3

Factor $x$ out of $x (20) + x (- (- 85 + 33 x))$ .

$\frac{x (20 - (- 85 + 33 x))}{40}$

Step 5.2

Apply the distributive property.

$\frac{x (20 - - 85 - (33 x))}{40}$

Step 5.3

Multiply $- 1$ by $- 85$ .

$\frac{x (20 + 85 - (33 x))}{40}$

Step 5.4

Multiply $33$ by $- 1$ .

$\frac{x (20 + 85 - 33 x)}{40}$

Step 5.5

Add $20$ and $85$ .

$\frac{x (105 - 33 x)}{40}$

Step 5.6

Factor $3$ out of $105 - 33 x$ .

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Step 5.6.1

Factor $3$ out of $105$ .

$\frac{x (3 (35) - 33 x)}{40}$

Step 5.6.2

Factor $3$ out of $- 33 x$ .

$\frac{x (3 (35) + 3 (- 11 x))}{40}$

Step 5.6.3

Factor $3$ out of $3 (35) + 3 (- 11 x)$ .

$\frac{x (3 (35 - 11 x))}{40}$

$\frac{x \cdot 3 (35 - 11 x)}{40}$

Step 6

Move $3$ to the left of $x$ .

$\frac{3 x (35 - 11 x)}{40}$