Practicing Success

Target Exam

CUET

Subject

General Test

Chapter

Quantitative Reasoning

Topic

Algebra

Question:

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

Options:

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

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

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

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

Correct Answer:

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

Explanation:

(a + b)3 = a3 + b3 + 3ab(a+b)

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

So by expanding this cubic equation we get,

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