Solve (9m-5m/3)^2=?

$$( 9 m - \frac { 5 m } { 3 } ) ^ { 2 } = ?$$

Evaluate

$$\frac{484m^{2}}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9m times \frac{3}{3}.

$$\left(\frac{3\times 9m}{3}-\frac{5m}{3}\right)^{2}$$

Since \frac{3\times 9m}{3} and \frac{5m}{3} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3\times 9m-5m}{3}\right)^{2}$$

Do the multiplications in 3\times 9m-5m.

$$\left(\frac{27m-5m}{3}\right)^{2}$$

Combine like terms in 27m-5m.

$$\left(\frac{22m}{3}\right)^{2}$$

To raise \frac{22m}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(22m\right)^{2}}{3^{2}}$$

Expand \left(22m\right)^{2}.

$$\frac{22^{2}m^{2}}{3^{2}}$$

Calculate 22 to the power of 2 and get 484.

$$\frac{484m^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{484m^{2}}{9}$$

Expand

$$\frac{484m^{2}}{9}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 9m times \frac{3}{3}.

$$\left(\frac{3\times 9m}{3}-\frac{5m}{3}\right)^{2}$$

Since \frac{3\times 9m}{3} and \frac{5m}{3} have the same denominator, subtract them by subtracting their numerators.

$$\left(\frac{3\times 9m-5m}{3}\right)^{2}$$

Do the multiplications in 3\times 9m-5m.

$$\left(\frac{27m-5m}{3}\right)^{2}$$

Combine like terms in 27m-5m.

$$\left(\frac{22m}{3}\right)^{2}$$

To raise \frac{22m}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(22m\right)^{2}}{3^{2}}$$

Expand \left(22m\right)^{2}.

$$\frac{22^{2}m^{2}}{3^{2}}$$

Calculate 22 to the power of 2 and get 484.

$$\frac{484m^{2}}{3^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{484m^{2}}{9}$$