Solve (x/2-5)^2-(x/2+5)^2

$$( \frac { x } { 2 } - 5 ) ^ { 2 } - ( \frac { x } { 2 } + 5 ) ^ { 2 }$$

Evaluate

$$-10x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

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

Since \frac{x}{2} and \frac{5\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-5\times 2.

$$\left(\frac{x-10}{2}\right)^{2}-\left(\frac{x}{2}+5\right)^{2}$$

To raise \frac{x-10}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x}{2}+5\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x}{2}+\frac{5\times 2}{2}\right)^{2}$$

Since \frac{x}{2} and \frac{5\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x+5\times 2}{2}\right)^{2}$$

Do the multiplications in x+5\times 2.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x+10}{2}\right)^{2}$$

To raise \frac{x+10}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\frac{\left(x+10\right)^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\frac{\left(x+10\right)^{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{\left(x-10\right)^{2}}{4}-\frac{\left(x+10\right)^{2}}{4}$$

Since \frac{\left(x-10\right)^{2}}{4} and \frac{\left(x+10\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-10\right)^{2}-\left(x+10\right)^{2}}{4}$$

Do the multiplications in \left(x-10\right)^{2}-\left(x+10\right)^{2}.

$$\frac{x^{2}-20x+100-x^{2}-20x-100}{4}$$

Combine like terms in x^{2}-20x+100-x^{2}-20x-100.

$$\frac{-40x}{4}$$

Divide -40x by 4 to get -10x.

$$-10x$$

Expand

$$-10x$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

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

Since \frac{x}{2} and \frac{5\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-5\times 2.

$$\left(\frac{x-10}{2}\right)^{2}-\left(\frac{x}{2}+5\right)^{2}$$

To raise \frac{x-10}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x}{2}+5\right)^{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5 times \frac{2}{2}.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x}{2}+\frac{5\times 2}{2}\right)^{2}$$

Since \frac{x}{2} and \frac{5\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x+5\times 2}{2}\right)^{2}$$

Do the multiplications in x+5\times 2.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\left(\frac{x+10}{2}\right)^{2}$$

To raise \frac{x+10}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\frac{\left(x+10\right)^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(x-10\right)^{2}}{2^{2}}-\frac{\left(x+10\right)^{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Expand 2^{2}.

$$\frac{\left(x-10\right)^{2}}{4}-\frac{\left(x+10\right)^{2}}{4}$$

Since \frac{\left(x-10\right)^{2}}{4} and \frac{\left(x+10\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\left(x-10\right)^{2}-\left(x+10\right)^{2}}{4}$$

Do the multiplications in \left(x-10\right)^{2}-\left(x+10\right)^{2}.

$$\frac{x^{2}-20x+100-x^{2}-20x-100}{4}$$

Combine like terms in x^{2}-20x+100-x^{2}-20x-100.

$$\frac{-40x}{4}$$

Divide -40x by 4 to get -10x.

$$-10x$$