Solve (2/7l-1/4m)(2/7l-1/4m)

$$( \frac { 2 } { 7 } l - \frac { 1 } { 4 } m ) ( \frac { 2 } { 7 } l - \frac { 1 } { 4 } m )$$

Evaluate

$$\frac{\left(8l-7m\right)^{2}}{784}$$

Solution Steps

Multiply \frac{2}{7}l-\frac{1}{4}m and \frac{2}{7}l-\frac{1}{4}m to get \left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}.

$$\left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}.

$$\frac{4}{49}l^{2}-\frac{1}{7}lm+\frac{1}{16}m^{2}$$

Expand

$$-\frac{lm}{7}+\frac{4l^{2}}{49}+\frac{m^{2}}{16}$$

Solution Steps

Multiply \frac{2}{7}l-\frac{1}{4}m and \frac{2}{7}l-\frac{1}{4}m to get \left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}.

$$\left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(\frac{2}{7}l-\frac{1}{4}m\right)^{2}.

$$\frac{4}{49}l^{2}-\frac{1}{7}lm+\frac{1}{16}m^{2}$$