Algebra Examples

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

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 $2$ .

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

Step 1.1.2

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

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

Step 1.1.3

Apply the product rule to $\frac{1}{2}$ .

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

Step 1.1.4

One to any power is one.

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

Step 1.1.5

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

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

Step 1.1.6

Cancel the common factor of $4$ .

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Step 1.1.6.1

Factor $4$ out of $- 4$ .

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

Step 1.1.6.2

Cancel the common factor.

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

Step 1.1.6.3

Rewrite the expression.

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

Step 1.2

Subtract $1$ from $- 27$ .

$4 \cdot - 28 + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.3

Multiply $4$ by $- 28$ .

$- 112 + 3 (\frac{2}{6}) - \sqrt{4}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Factor $3$ out of $6$ .

$- 112 + 3 \frac{2}{3 (2)} - \sqrt{4}$

Step 1.4.2

Cancel the common factor.

$- 112 + 3 \frac{2}{3 \cdot 2} - \sqrt{4}$

Step 1.4.3

Rewrite the expression.

$- 112 + \frac{2}{2} - \sqrt{4}$

Step 1.5

Divide $2$ by $2$ .

$- 112 + 1 - \sqrt{4}$

Step 1.6

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

$- 112 + 1 - \sqrt{2^{2}}$

Step 1.7

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

$- 112 + 1 - 1 \cdot 2$

Step 1.8

Multiply $- 1$ by $2$ .

$- 112 + 1 - 2$

Step 2

Simplify by adding and subtracting.

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Step 2.1

Add $- 112$ and $1$ .

$- 111 - 2$

Step 2.2

Subtract $2$ from $- 111$ .

$- 113$