Solve (2a+b/2+2a-b/2)^2

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

Evaluate

$$4a^{2}$$

Short Solution Steps

Since \frac{2a+b}{2} and \frac{2a-b}{2} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2a+b+2a-b.

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

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

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

Expand \left(4a\right)^{2}.

$$\frac{4^{2}a^{2}}{2^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16a^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16a^{2}}{4}$$

Divide 16a^{2} by 4 to get 4a^{2}.

$$4a^{2}$$

Expand

$$4a^{2}$$

Short Solution Steps

Since \frac{2a+b}{2} and \frac{2a-b}{2} have the same denominator, add them by adding their numerators.

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

Combine like terms in 2a+b+2a-b.

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

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

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

Expand \left(4a\right)^{2}.

$$\frac{4^{2}a^{2}}{2^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16a^{2}}{2^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{16a^{2}}{4}$$

Divide 16a^{2} by 4 to get 4a^{2}.

$$4a^{2}$$