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

Given:

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

To do:

We have to simplify \( \left(\frac{2}{7} l-\frac{1}{4} m\right)\left(\frac{2}{7} l-\frac{1}{4} m\right) \).

Solution:

We know that,

$(a-b)^2=a^2-2ab+b^2$

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

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

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

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

Therefore, $(\frac{2}{7} l-\frac{1}{4} m)(\frac{2}{7} l-\frac{1}{4} m)=\frac{4}{49}l^2-\frac{1}{7}lm+\frac{1}{16}m^2$.

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Updated on: 10-Oct-2022

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