Solve (3x-2/4)^2+(3x+2/4)^2

$$( \frac { 3 x - 2 } { 4 } ) ^ { 2 } + ( \frac { 3 x + 2 } { 4 } ) ^ { 2 }$$

Evaluate

$$\frac{9x^{2}}{8}+\frac{1}{2}$$

Short Solution Steps

To raise \frac{3x-2}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{4^{2}}+\left(\frac{3x+2}{4}\right)^{2}$$

To raise \frac{3x+2}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{4^{2}}+\frac{\left(3x+2\right)^{2}}{4^{2}}$$

Since \frac{\left(3x-2\right)^{2}}{4^{2}} and \frac{\left(3x+2\right)^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-2\right)^{2}+\left(3x+2\right)^{2}}{4^{2}}$$

Do the multiplications in \left(3x-2\right)^{2}+\left(3x+2\right)^{2}.

$$\frac{9x^{2}-12x+4+9x^{2}+12x+4}{4^{2}}$$

Combine like terms in 9x^{2}-12x+4+9x^{2}+12x+4.

$$\frac{18x^{2}+8}{4^{2}}$$

Expand 4^{2}.

$$\frac{18x^{2}+8}{16}$$

Expand

$$\frac{9x^{2}}{8}+\frac{1}{2}$$

Short Solution Steps

To raise \frac{3x-2}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{4^{2}}+\left(\frac{3x+2}{4}\right)^{2}$$

To raise \frac{3x+2}{4} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x-2\right)^{2}}{4^{2}}+\frac{\left(3x+2\right)^{2}}{4^{2}}$$

Since \frac{\left(3x-2\right)^{2}}{4^{2}} and \frac{\left(3x+2\right)^{2}}{4^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(3x-2\right)^{2}+\left(3x+2\right)^{2}}{4^{2}}$$

Do the multiplications in \left(3x-2\right)^{2}+\left(3x+2\right)^{2}.

$$\frac{9x^{2}-12x+4+9x^{2}+12x+4}{4^{2}}$$

Combine like terms in 9x^{2}-12x+4+9x^{2}+12x+4.

$$\frac{18x^{2}+8}{4^{2}}$$

Expand 4^{2}.

$$\frac{18x^{2}+8}{16}$$