Solve:$\left(\frac{2}{5}a\ -\ \frac{1}{2}b\right)(10a\ -\ 8b)$

Given: $\left(\frac{2}{5}a\ -\ \frac{1}{2}b\right)(10a\ -\ 8b)$

To find: Here we have to find the value of the given expression $\left(\frac{2}{5}a\ -\ \frac{1}{2}b\right)(10a\ -\ 8b)$.

Solution:

$\left(\frac{2}{5} a\ -\ \frac{1}{2} b\right) (10a\ -\ 8b)$

$=\ 10a\left(\frac{2}{5} a\ -\ \frac{1}{2} b\right) \ -\ 8b\left(\frac{2}{5} a\ -\ \frac{1}{2} b\right)$

$=\ \left( 10a\ \times \ \frac{2}{5} a\right) \ -\ \left( 10a\ \times \ \frac{1}{2} b\right) \ -\ \left( 8b\ \times \ \frac{2}{5} a\right) \ -\ \left( 8b\ \times \ \frac{1}{2} b\right)$

$=\ ( 2a\ \times \ 2a) \ -\ ( 5a\ \times \ b) \ -\ \left( 8b\ \times \ \frac{2}{5} a\right) \ -\ ( 4b\ \times \ b)$

$=\ 4a\ -\ 5ab\ -\ \frac{16}{5} ab\ -\ 4b^{2}$

$=\ 4a\ -\ \left( 5\ +\ \frac{16}{5}\right) ab\ -\ 4b^{2}$

$=\ 4a\ -\ \left(\frac{25\ +\ 16}{5}\right) ab\ -\ 4b^{2}$

$=\ \mathbf{4a\ -\ \frac{41}{5} ab\ -\ 4b^{2}}$

So, value of the given expression is $4a\ -\ \frac{41}{5} ab\ -\ 4b^{2}$.

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Updated on: 10-Oct-2022

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