Evaluate (4((2-5)^3-4(1/2)^2)+3(2/6))- square root of 4

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

Simplify each term.

Subtract $5$ from $2$ .

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

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

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

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

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

One to any power is one.

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Subtract $1$ from $- 27$ .

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

Multiply $4$ by $- 28$ .

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

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $2$ by $2$ .

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

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

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

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

$- 112 + 1 - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- 112 + 1 - 2$

Simplify by adding and subtracting.

Add $- 112$ and $1$ .

$- 111 - 2$

Subtract $2$ from $- 111$ .

$- 113$