Evaluate (57+72-|28-(16+25)|^2+8)-(|-20|)÷4

$(57 + 72 - {| 28 - (16 + 25) |}^{2} + 8) - | - 20 | \div 4$

Step 1

Find the common denominator.

Write $57$ as a fraction with denominator $1$ .

$\frac{57}{1} + 72 - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Multiply $\frac{57}{1}$ by $\frac{4}{4}$ .

$\frac{57}{1} \cdot \frac{4}{4} + 72 - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Multiply $\frac{57}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + 72 - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Write $72$ as a fraction with denominator $1$ .

$\frac{57 \cdot 4}{4} + \frac{72}{1} - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Multiply $\frac{72}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72}{1} \cdot \frac{4}{4} - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Multiply $\frac{72}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} - {| 28 - (16 + 25) |}^{2} + 8 - | - 20 | \div 4$

Write $- {| 28 - (16 + 25) |}^{2}$ as a fraction with denominator $1$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2}}{1} + 8 - | - 20 | \div 4$

Multiply $\frac{- {| 28 - (16 + 25) |}^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2}}{1} \cdot \frac{4}{4} + 8 - | - 20 | \div 4$

Multiply $\frac{- {| 28 - (16 + 25) |}^{2}}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2} \cdot 4}{4} + 8 - | - 20 | \div 4$

Write $8$ as a fraction with denominator $1$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2} \cdot 4}{4} + \frac{8}{1} - | - 20 | \div 4$

Multiply $\frac{8}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2} \cdot 4}{4} + \frac{8}{1} \cdot \frac{4}{4} - | - 20 | \div 4$

Multiply $\frac{8}{1}$ by $\frac{4}{4}$ .

$\frac{57 \cdot 4}{4} + \frac{72 \cdot 4}{4} + \frac{- {| 28 - (16 + 25) |}^{2} \cdot 4}{4} + \frac{8 \cdot 4}{4} - | - 20 | \div 4$

Step 2

Combine the numerators over the common denominator.

$\frac{57 \cdot 4 + 72 \cdot 4 - {| 28 - (16 + 25) |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Step 3

Simplify each term.

Multiply $57$ by $4$ .

$\frac{228 + 72 \cdot 4 - {| 28 - (16 + 25) |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Multiply $72$ by $4$ .

$\frac{228 + 288 - {| 28 - (16 + 25) |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Simplify each term.

Add $16$ and $25$ .

$\frac{228 + 288 - {| 28 - 1 \cdot 41 |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Multiply $- 1$ by $41$ .

$\frac{228 + 288 - {| 28 - 41 |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Subtract $41$ from $28$ .

$\frac{228 + 288 - {| - 13 |}^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

The absolute value is the distance between a number and zero. The distance between $- 13$ and $0$ is $13$ .

$\frac{228 + 288 - 13^{2} \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Raise $13$ to the power of $2$ .

$\frac{228 + 288 - 1 \cdot 169 \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Multiply $- 1 \cdot 169 \cdot 4$ .

Multiply $- 1$ by $169$ .

$\frac{228 + 288 - 169 \cdot 4 + 8 \cdot 4 - | - 20 |}{4}$

Multiply $- 169$ by $4$ .

$\frac{228 + 288 - 676 + 8 \cdot 4 - | - 20 |}{4}$

Multiply $8$ by $4$ .

$\frac{228 + 288 - 676 + 32 - | - 20 |}{4}$

The absolute value is the distance between a number and zero. The distance between $- 20$ and $0$ is $20$ .

$\frac{228 + 288 - 676 + 32 - 1 \cdot 20}{4}$

Multiply $- 1$ by $20$ .

$\frac{228 + 288 - 676 + 32 - 20}{4}$

Step 4

Simplify the expression.

Add $228$ and $288$ .

$\frac{516 - 676 + 32 - 20}{4}$

Subtract $676$ from $516$ .

$\frac{- 160 + 32 - 20}{4}$

Add $- 160$ and $32$ .

$\frac{- 128 - 20}{4}$

Subtract $20$ from $- 128$ .

$\frac{- 148}{4}$

Divide $- 148$ by $4$ .

$- 37$

Evaluate (57+72-|28-(16+25)|^2+8)-(|-20|)÷4

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