Solve (2^3-x/2-3-1)^2-sqrt{3}*sqrt{1/3}+1-3/3/2:frac{5}{1}

$$( \frac { 2 ^ { 3 } - x } { 2 - 3 } - 1 ) ^ { 2 } - \sqrt { 3 } \times \sqrt { \frac { 1 } { 3 } } + \frac { 1 - \frac { 3 } { 3 } } { 2 } : \frac { 5 } { 1 }$$

Factor

$$\left(x-10\right)\left(x-8\right)$$

Solution Steps

Divide 3 by 3 to get 1.

$$factor(\left(\frac{2^{3}-x}{2-3}-1\right)^{2}-\sqrt{3}\sqrt{\frac{1}{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Calculate 2 to the power of 3 and get 8.

$$factor(\left(\frac{8-x}{2-3}-1\right)^{2}-\sqrt{3}\sqrt{\frac{1}{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Subtract 3 from 2 to get -1.

$$factor(\left(\frac{8-x}{-1}-1\right)^{2}-\sqrt{3}\sqrt{\frac{1}{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Anything divided by -1 gives its opposite. To find the opposite of 8-x, find the opposite of each term.

$$factor(\left(-8+x-1\right)^{2}-\sqrt{3}\sqrt{\frac{1}{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Subtract 1 from -8 to get -9.

$$factor(\left(-9+x\right)^{2}-\sqrt{3}\sqrt{\frac{1}{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Rewrite the square root of the division \sqrt{\frac{1}{3}} as the division of square roots \frac{\sqrt{1}}{\sqrt{3}}.

$$factor(\left(-9+x\right)^{2}-\sqrt{3}\times \frac{\sqrt{1}}{\sqrt{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Calculate the square root of 1 and get 1.

$$factor(\left(-9+x\right)^{2}-\sqrt{3}\times \frac{1}{\sqrt{3}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Rationalize the denominator of \frac{1}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$factor(\left(-9+x\right)^{2}-\sqrt{3}\times \frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

The square of \sqrt{3} is 3.

$$factor(\left(-9+x\right)^{2}-\sqrt{3}\times \frac{\sqrt{3}}{3}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Express \sqrt{3}\times \frac{\sqrt{3}}{3} as a single fraction.

$$factor(\left(-9+x\right)^{2}-\frac{\sqrt{3}\sqrt{3}}{3}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$factor(\left(-9+x\right)^{2}-\frac{3}{3}+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Divide 3 by 3 to get 1.

$$factor(\left(-9+x\right)^{2}-1+\frac{\frac{1-1}{2}}{\frac{5}{1}})$$

Divide \frac{1-1}{2} by \frac{5}{1} by multiplying \frac{1-1}{2} by the reciprocal of \frac{5}{1}.

$$factor(\left(-9+x\right)^{2}-1+\frac{1-1}{2\times 5})$$

Subtract 1 from 1 to get 0.

$$factor(\left(-9+x\right)^{2}-1+\frac{0}{2\times 5})$$

Multiply 2 and 5 to get 10.

$$factor(\left(-9+x\right)^{2}-1+\frac{0}{10})$$

Zero divided by any non-zero number gives zero.

$$factor(\left(-9+x\right)^{2}-1+0)$$

Add -1 and 0 to get -1.

$$factor(\left(-9+x\right)^{2}-1)$$

The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x-8\right)$$

Evaluate

$$\left(x-10\right)\left(x-8\right)$$