6.(iv) Write the following cube in expanded form:

    (iv)    \left[x - \frac{2}{3} y\right ]^3

Answers (1)

Given is  \left[x - \frac{2}{3} y\right ]^3

We will use identity

(a-b)^3=a^3-b^3-3a^2b+3ab^2

Here,  a=x \ and \ \ b= \frac{2y}{3}

Therefore, 

\left[x - \frac{2}{3} y\right ]^3 = x^3-\left(\frac{2y}{3} \right )^3-3.x^2.\frac{2y}{3}+3.x.\left(\frac{2y}{3} \right )^2

                      = x^3-\frac{8y^3}{27}-2x^2y+\frac{4xy^2}{3}

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