Algebra Examples

$(4 ({(2 - 5)}^{3} - 4 {(\frac{1}{2} - \frac{5}{3})}^{2}) + 3 (\frac{2}{6})) - \sqrt{4}$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Subtract $5$ from $2$ .

$4 ({(- 3)}^{3} - 4 {(\frac{1}{2} - \frac{5}{3})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.2

Raise $- 3$ to the power of $3$ .

$4 (- 27 - 4 {(\frac{1}{2} - \frac{5}{3})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.3

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 (- 27 - 4 {(\frac{1}{2} \cdot \frac{3}{3} - \frac{5}{3})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.4

To write $- \frac{5}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$4 (- 27 - 4 {(\frac{1}{2} \cdot \frac{3}{3} - \frac{5}{3} \cdot \frac{2}{2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.5

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.1.5.1

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$4 (- 27 - 4 {(\frac{3}{2 \cdot 3} - \frac{5}{3} \cdot \frac{2}{2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.5.2

Multiply $2$ by $3$ .

$4 (- 27 - 4 {(\frac{3}{6} - \frac{5}{3} \cdot \frac{2}{2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.5.3

Multiply $\frac{5}{3}$ by $\frac{2}{2}$ .

$4 (- 27 - 4 {(\frac{3}{6} - \frac{5 \cdot 2}{3 \cdot 2})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.5.4

Multiply $3$ by $2$ .

$4 (- 27 - 4 {(\frac{3}{6} - \frac{5 \cdot 2}{6})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.6

Combine the numerators over the common denominator.

$4 (- 27 - 4 {(\frac{3 - 5 \cdot 2}{6})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.7

Simplify the numerator.

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Step 1.1.7.1

Multiply $- 5$ by $2$ .

$4 (- 27 - 4 {(\frac{3 - 10}{6})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.7.2

Subtract $10$ from $3$ .

$4 (- 27 - 4 {(\frac{- 7}{6})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.8

Move the negative in front of the fraction.

$4 (- 27 - 4 {(- \frac{7}{6})}^{2}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.9

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.9.1

Apply the product rule to $- \frac{7}{6}$ .

$4 (- 27 - 4 ({(- 1)}^{2} {(\frac{7}{6})}^{2})) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.9.2

Apply the product rule to $\frac{7}{6}$ .

$4 (- 27 - 4 ({(- 1)}^{2} \frac{7^{2}}{6^{2}})) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.10

Raise $- 1$ to the power of $2$ .

$4 (- 27 - 4 (1 \frac{7^{2}}{6^{2}})) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.11

Multiply $\frac{7^{2}}{6^{2}}$ by $1$ .

$4 (- 27 - 4 \frac{7^{2}}{6^{2}}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.12

Raise $7$ to the power of $2$ .

$4 (- 27 - 4 \frac{49}{6^{2}}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.13

Raise $6$ to the power of $2$ .

$4 (- 27 - 4 (\frac{49}{36})) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.14

Cancel the common factor of $4$ .

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Step 1.1.14.1

Factor $4$ out of $- 4$ .

$4 (- 27 + 4 (- 1) \frac{49}{36}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.14.2

Factor $4$ out of $36$ .

$4 (- 27 + 4 \cdot - 1 \frac{49}{4 \cdot 9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.14.3

Cancel the common factor.

$4 (- 27 + 4 \cdot - 1 \frac{49}{4 \cdot 9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.14.4

Rewrite the expression.

$4 (- 27 - 1 (\frac{49}{9})) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.1.15

Rewrite $- 1 (\frac{49}{9})$ as $- (\frac{49}{9})$ .

$4 (- 27 - \frac{49}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.2

To write $- 27$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$4 (- 27 \cdot \frac{9}{9} - \frac{49}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.3

Combine $- 27$ and $\frac{9}{9}$ .

$4 (\frac{- 27 \cdot 9}{9} - \frac{49}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.4

Combine the numerators over the common denominator.

$4 \frac{- 27 \cdot 9 - 49}{9} + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 27$ by $9$ .

$4 \frac{- 243 - 49}{9} + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.5.2

Subtract $49$ from $- 243$ .

$4 (\frac{- 292}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.6

Move the negative in front of the fraction.

$4 (- \frac{292}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.7

Multiply $4 (- \frac{292}{9})$ .

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Step 1.7.1

Multiply $- 1$ by $4$ .

$- 4 (\frac{292}{9}) + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.7.2

Combine $- 4$ and $\frac{292}{9}$ .

$\frac{- 4 \cdot 292}{9} + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.7.3

Multiply $- 4$ by $292$ .

$\frac{- 1168}{9} + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.8

Move the negative in front of the fraction.

$- \frac{1168}{9} + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Factor $3$ out of $6$ .

$- \frac{1168}{9} + 3 \frac{2}{3 (2)} - \sqrt{4}$

Step 1.9.2

Cancel the common factor.

$- \frac{1168}{9} + 3 \frac{2}{3 \cdot 2} - \sqrt{4}$

Step 1.9.3

Rewrite the expression.

$- \frac{1168}{9} + \frac{2}{2} - \sqrt{4}$

Step 1.10

Divide $2$ by $2$ .

$- \frac{1168}{9} + 1 - \sqrt{4}$

Step 1.11

Rewrite $4$ as $2^{2}$ .

$- \frac{1168}{9} + 1 - \sqrt{2^{2}}$

Step 1.12

Pull terms out from under the radical, assuming positive real numbers.

$- \frac{1168}{9} + 1 - 1 \cdot 2$

Step 1.13

Multiply $- 1$ by $2$ .

$- \frac{1168}{9} + 1 - 2$

Step 2

Find the common denominator.

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Step 2.1

Write $1$ as a fraction with denominator $1$ .

$- \frac{1168}{9} + \frac{1}{1} - 2$

Step 2.2

Multiply $\frac{1}{1}$ by $\frac{9}{9}$ .

$- \frac{1168}{9} + \frac{1}{1} \cdot \frac{9}{9} - 2$

Step 2.3

Multiply $\frac{1}{1}$ by $\frac{9}{9}$ .

$- \frac{1168}{9} + \frac{9}{9} - 2$

Step 2.4

Write $- 2$ as a fraction with denominator $1$ .

$- \frac{1168}{9} + \frac{9}{9} + \frac{- 2}{1}$

Step 2.5

Multiply $\frac{- 2}{1}$ by $\frac{9}{9}$ .

$- \frac{1168}{9} + \frac{9}{9} + \frac{- 2}{1} \cdot \frac{9}{9}$

Step 2.6

Multiply $\frac{- 2}{1}$ by $\frac{9}{9}$ .

$- \frac{1168}{9} + \frac{9}{9} + \frac{- 2 \cdot 9}{9}$

Step 3

Combine the numerators over the common denominator.

$\frac{- 1168 + 9 - 2 \cdot 9}{9}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $- 2$ by $9$ .

$\frac{- 1168 + 9 - 18}{9}$

Step 4.2

Add $- 1168$ and $9$ .

$\frac{- 1159 - 18}{9}$

Step 4.3

Subtract $18$ from $- 1159$ .

$\frac{- 1177}{9}$

Step 4.4

Move the negative in front of the fraction.

$- \frac{1177}{9}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1177}{9}$

Decimal Form:

$- 130.\overline{7}$

Mixed Number Form:

$- 130 \frac{7}{9}$