Evaluate (4+((2-5)^2-4(7-5)^3+2(15/3)))- square root of 16

$(4 + ({(2 - 5)}^{2} - 4 {(7 - 5)}^{3} + 2 (\frac{15}{3}))) - \sqrt{16}$

Step 1

Remove parentheses.

$4 + {(2 - 5)}^{2} - 4 {(7 - 5)}^{3} + 2 (\frac{15}{3}) - \sqrt{16}$

Step 2

Simplify each term.

Subtract $5$ from $2$ .

$4 + {(- 3)}^{2} - 4 {(7 - 5)}^{3} + 2 (\frac{15}{3}) - \sqrt{16}$

Raise $- 3$ to the power of $2$ .

$4 + 9 - 4 {(7 - 5)}^{3} + 2 (\frac{15}{3}) - \sqrt{16}$

Subtract $5$ from $7$ .

$4 + 9 - 4 \cdot 2^{3} + 2 (\frac{15}{3}) - \sqrt{16}$

Raise $2$ to the power of $3$ .

$4 + 9 - 4 \cdot 8 + 2 (\frac{15}{3}) - \sqrt{16}$

Multiply $- 4$ by $8$ .

$4 + 9 - 32 + 2 (\frac{15}{3}) - \sqrt{16}$

Divide $15$ by $3$ .

$4 + 9 - 32 + 2 \cdot 5 - \sqrt{16}$

Multiply $2$ by $5$ .

$4 + 9 - 32 + 10 - \sqrt{16}$

Rewrite $16$ as $4^{2}$ .

$4 + 9 - 32 + 10 - \sqrt{4^{2}}$

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

$4 + 9 - 32 + 10 - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$4 + 9 - 32 + 10 - 4$

Step 3

Simplify by adding and subtracting.

Add $4$ and $9$ .

$13 - 32 + 10 - 4$

Subtract $32$ from $13$ .

$- 19 + 10 - 4$

Add $- 19$ and $10$ .

$- 9 - 4$

Subtract $4$ from $- 9$ .

$- 13$