Simplify (4((3-5)^2-2(5/2-6/4)^3)+6(8/12))- square root of 25

$(4 ({(3 - 5)}^{2} - 2 {(\frac{5}{2} - \frac{6}{4})}^{3}) + 6 (\frac{8}{12})) - \sqrt{25}$

Simplify each term.

Subtract $5$ from $3$ .

$4 ({(- 2)}^{2} - 2 {(\frac{5}{2} - \frac{6}{4})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

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

$4 (4 - 2 {(\frac{5}{2} - \frac{6}{4})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Cancel the common factor of $6$ and $4$ .

Factor $2$ out of $6$ .

$4 (4 - 2 {(\frac{5}{2} - \frac{2 (3)}{4})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Cancel the common factors.

Factor $2$ out of $4$ .

$4 (4 - 2 {(\frac{5}{2} - \frac{2 \cdot 3}{2 \cdot 2})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Cancel the common factor.

$4 (4 - 2 {(\frac{5}{2} - \frac{2 \cdot 3}{2 \cdot 2})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Rewrite the expression.

$4 (4 - 2 {(\frac{5}{2} - \frac{3}{2})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Combine the numerators over the common denominator.

$4 (4 - 2 {(\frac{5 - 3}{2})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Subtract $3$ from $5$ .

$4 (4 - 2 {(\frac{2}{2})}^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

Divide $2$ by $2$ .

$4 (4 - 2 \cdot 1^{3}) + 6 (\frac{8}{12}) - \sqrt{25}$

One to any power is one.

$4 (4 - 2 \cdot 1) + 6 (\frac{8}{12}) - \sqrt{25}$

Multiply $- 2$ by $1$ .

$4 (4 - 2) + 6 (\frac{8}{12}) - \sqrt{25}$

Subtract $2$ from $4$ .

$4 \cdot 2 + 6 (\frac{8}{12}) - \sqrt{25}$

Multiply $4$ by $2$ .

$8 + 6 (\frac{8}{12}) - \sqrt{25}$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$8 + 6 \frac{8}{6 (2)} - \sqrt{25}$

Cancel the common factor.

$8 + 6 \frac{8}{6 \cdot 2} - \sqrt{25}$

Rewrite the expression.

$8 + \frac{8}{2} - \sqrt{25}$

Divide $8$ by $2$ .

$8 + 4 - \sqrt{25}$

Rewrite $25$ as $5^{2}$ .

$8 + 4 - \sqrt{5^{2}}$

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

$8 + 4 - 1 \cdot 5$

Multiply $- 1$ by $5$ .

$8 + 4 - 5$

Simplify by adding and subtracting.

Add $8$ and $4$ .

$12 - 5$

Subtract $5$ from $12$ .

$7$

Simplify (4((3-5)^2-2(5/2-6/4)^3)+6(8/12))- square root of 25

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