Solve 81-4(x-18/4)^2

$$81 - 4 ( \frac { x - 18 } { 4 } ) ^ { 2 }$$

Evaluate

$$-\frac{x^{2}}{4}+9x$$

Short Solution Steps

To raise \frac{x-18}{4} to a power, raise both numerator and denominator to the power and then divide.

$$81-4\times \frac{\left(x-18\right)^{2}}{4^{2}}$$

Express 4\times \frac{\left(x-18\right)^{2}}{4^{2}} as a single fraction.

$$81-\frac{4\left(x-18\right)^{2}}{4^{2}}$$

Cancel out 4 in both numerator and denominator.

$$81-\frac{\left(x-18\right)^{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81 times \frac{4}{4}.

$$\frac{81\times 4}{4}-\frac{\left(x-18\right)^{2}}{4}$$

Since \frac{81\times 4}{4} and \frac{\left(x-18\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81\times 4-\left(x-18\right)^{2}}{4}$$

Do the multiplications in 81\times 4-\left(x-18\right)^{2}.

$$\frac{324-x^{2}+36x-324}{4}$$

Combine like terms in 324-x^{2}+36x-324.

$$\frac{-x^{2}+36x}{4}$$

Expand

$$-\frac{x^{2}}{4}+9x$$

Short Solution Steps

To raise \frac{x-18}{4} to a power, raise both numerator and denominator to the power and then divide.

$$81-4\times \frac{\left(x-18\right)^{2}}{4^{2}}$$

Express 4\times \frac{\left(x-18\right)^{2}}{4^{2}} as a single fraction.

$$81-\frac{4\left(x-18\right)^{2}}{4^{2}}$$

Cancel out 4 in both numerator and denominator.

$$81-\frac{\left(x-18\right)^{2}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 81 times \frac{4}{4}.

$$\frac{81\times 4}{4}-\frac{\left(x-18\right)^{2}}{4}$$

Since \frac{81\times 4}{4} and \frac{\left(x-18\right)^{2}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{81\times 4-\left(x-18\right)^{2}}{4}$$

Do the multiplications in 81\times 4-\left(x-18\right)^{2}.

$$\frac{324-x^{2}+36x-324}{4}$$

Combine like terms in 324-x^{2}+36x-324.

$$\frac{-x^{2}+36x}{4}$$