Simplify 4-(3+1)^2-6÷2+4

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

Find the common denominator.

Write $4$ as a fraction with denominator $1$ .

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

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

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

Write $- {(3 + 1)}^{2}$ as a fraction with denominator $1$ .

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

Multiply $\frac{- {(3 + 1)}^{2}}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{- {(3 + 1)}^{2}}{1}$ by $\frac{2}{2}$ .

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

Write $4$ as a fraction with denominator $1$ .

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

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

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

Multiply $\frac{4}{1}$ by $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Multiply $4$ by $2$ .

$\frac{8 - {(3 + 1)}^{2} \cdot 2 - 6 + 4 \cdot 2}{2}$

Add $3$ and $1$ .

$\frac{8 - 4^{2} \cdot 2 - 6 + 4 \cdot 2}{2}$

Raise $4$ to the power of $2$ .

$\frac{8 - 1 \cdot 16 \cdot 2 - 6 + 4 \cdot 2}{2}$

Multiply $- 1$ by $16$ .

$\frac{8 - 16 \cdot 2 - 6 + 4 \cdot 2}{2}$

Multiply $- 16$ by $2$ .

$\frac{8 - 32 - 6 + 4 \cdot 2}{2}$

Multiply $4$ by $2$ .

$\frac{8 - 32 - 6 + 8}{2}$

Simplify the expression.

Subtract $32$ from $8$ .

$\frac{- 24 - 6 + 8}{2}$

Subtract $6$ from $- 24$ .

$\frac{- 30 + 8}{2}$

Add $- 30$ and $8$ .

$\frac{- 22}{2}$

Divide $- 22$ by $2$ .

$- 11$