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Multiply:
$ \left(\frac{3}{5} x+\frac{1}{2} y\right) $ by $ \left(\frac{5}{6} x+4 y\right) $
To do:
We have to multiply \( \left(\frac{3}{5} x+\frac{1}{2} y\right) \) by \( \left(\frac{5}{6} x+4 y\right) \)
Solution:
We know that,
$(a+b)\times(c+d)=a(c+d)+b(c+d)$
Therefore,
$(\frac{3}{5} x+\frac{1}{2} y) \times(\frac{5}{6} x+4 y)=\frac{3}{5} x(\frac{5}{6} x+4 y)+\frac{1}{2} y(\frac{5}{6} x+4 y)$
$=\frac{3}{5} x \times \frac{5}{6} x+\frac{3}{5}x \times 4y+\frac{1}{2}y\times \frac{5}{6} x+\frac{1}{2}y \times 4 y$
$=\frac{1}{2} x^{2}+\frac{12}{5} x y+\frac{5}{12} x y+2 y^{2}$
$=\frac{1}{2} x^{2}+\frac{144 x y+25 x y}{60}+2 y^{2}$
$=\frac{1}{2} x^{2}+\frac{169}{60} x y+2 y^{2}$
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