Solve 4(a-4/2)^2+1

$$4 ( \frac { a - 4 } { 2 } ) ^ { 2 } + 1$$

Evaluate

$$\left(a-4\right)^{2}+1$$

Short Solution Steps

To raise \frac{a-4}{2} to a power, raise both numerator and denominator to the power and then divide.

$$4\times \frac{\left(a-4\right)^{2}}{2^{2}}+1$$

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

$$\frac{4\left(a-4\right)^{2}}{2^{2}}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2^{2}}{2^{2}}.

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

Since \frac{4\left(a-4\right)^{2}}{2^{2}} and \frac{2^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(a-4\right)^{2}+2^{2}.

$$\frac{4a^{2}-32a+64+2^{2}}{2^{2}}$$

Combine like terms in 4a^{2}-32a+64+2^{2}.

$$\frac{4a^{2}-32a+68}{2^{2}}$$

Expand 2^{2}.

$$\frac{4a^{2}-32a+68}{4}$$

Divide each term of 4a^{2}-32a+68 by 4 to get a^{2}-8a+17.

$$a^{2}-8a+17$$

Expand

$$a^{2}-8a+17$$

Short Solution Steps

To raise \frac{a-4}{2} to a power, raise both numerator and denominator to the power and then divide.

$$4\times \frac{\left(a-4\right)^{2}}{2^{2}}+1$$

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

$$\frac{4\left(a-4\right)^{2}}{2^{2}}+1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2^{2}}{2^{2}}.

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

Since \frac{4\left(a-4\right)^{2}}{2^{2}} and \frac{2^{2}}{2^{2}} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4\left(a-4\right)^{2}+2^{2}.

$$\frac{4a^{2}-32a+64+2^{2}}{2^{2}}$$

Combine like terms in 4a^{2}-32a+64+2^{2}.

$$\frac{4a^{2}-32a+68}{2^{2}}$$

Expand 2^{2}.

$$\frac{4a^{2}-32a+68}{4}$$

Divide each term of 4a^{2}-32a+68 by 4 to get a^{2}-8a+17.

$$a^{2}-8a+17$$