Question 61

Expand $$\left(\frac{x}{3} + \frac{y}{5}\right)^3$$

Solution

$$\left(\frac{x}{3} + \frac{y}{5}\right)^3$$

($$\because (a + b)^3 = a^3 + b^3 + 3ab(a + b)$$)

= $$(\frac{x}{3})^3 + (\frac{y}{5})^3 + 3(\frac{x}{3})(\frac{y}{5})(\frac{x}{3} + \frac{y}{5}) $$

= $$\frac{x^3}{27} + \frac{y^3}{125} + \frac{xy}{5} (\frac{x}{3} + \frac{y}{5}) $$

= $$\frac{x^3}{27} + \frac{y^3}{125} + \frac{x^2y}{15} + \frac{xy^2}{25} $$

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