Solve [[2l]^2-1/(5m)^2]

$$[ [ 2 l ] ^ { 2 } \frac { - 1 } { ( 5 m ) ^ { 2 } } ]$$

Evaluate

$$-\frac{4\times \left(\frac{l}{m}\right)^{2}}{25}$$

Solution Steps

Expand \left(2l\right)^{2}.

$$2^{2}l^{2}\times \frac{-1}{\left(5m\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$4l^{2}\times \frac{-1}{\left(5m\right)^{2}}$$

Expand \left(5m\right)^{2}.

$$4l^{2}\times \frac{-1}{5^{2}m^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4l^{2}\times \frac{-1}{25m^{2}}$$

Express 4\times \frac{-1}{25m^{2}} as a single fraction.

$$\frac{4\left(-1\right)}{25m^{2}}l^{2}$$

Multiply 4 and -1 to get -4.

$$\frac{-4}{25m^{2}}l^{2}$$

Express \frac{-4}{25m^{2}}l^{2} as a single fraction.

$$\frac{-4l^{2}}{25m^{2}}$$

Expand

$$-\frac{4\times \left(\frac{l}{m}\right)^{2}}{25}$$

Solution Steps

Expand \left(2l\right)^{2}.

$$2^{2}l^{2}\times \frac{-1}{\left(5m\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$4l^{2}\times \frac{-1}{\left(5m\right)^{2}}$$

Expand \left(5m\right)^{2}.

$$4l^{2}\times \frac{-1}{5^{2}m^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$4l^{2}\times \frac{-1}{25m^{2}}$$

Express 4\times \frac{-1}{25m^{2}} as a single fraction.

$$\frac{4\left(-1\right)}{25m^{2}}l^{2}$$

Multiply 4 and -1 to get -4.

$$\frac{-4}{25m^{2}}l^{2}$$

Express \frac{-4}{25m^{2}}l^{2} as a single fraction.

$$\frac{-4l^{2}}{25m^{2}}$$