Multiply: (3 5 x+1 2 y ) by (5 6 x+4y )

Question

Multiply:
$\big(\frac{3}{5}\text{x}+\frac{1}{2}\text{y}\big) \ \text{by} \ \big(\frac{5}{6}\text{x}+4\text{y}\big)$

✓

Answer

To multiply, we will use distributive law as follows:
$\big(\frac{3}{5}\text{x}+\frac{1}{2}\text{y}\big) \ \text{by} \ \big(\frac{5}{6}\text{x}+4\text{y}\big)$
$=\frac{3}{5}\text{x}\big(\frac{5}{6}\text{x}+4\text{y}\big)+\frac{1}{2}\text{y}\big(\frac{5}{6}\text{x}+4\text{y})$
$=\frac{1}{2}\text{x}^2+\frac{12}{5}\text{xy}+\frac{5}{12}\text{xy}+2\text{y}^2$
$=\frac{1}{2}\text{x}^2+\big(\frac{144+25}{60}\big)\text{xy}+2\text{y}^2$
$=\frac{1}{2}\text{x}^2+\frac{169}{60}\text{xy}+2\text{y}^2$
Thus, the answer is $=\frac{1}{2}\text{x}^2+\frac{169}{60}\text{xy}+2\text{y}^2.$

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