What is expand (1-y/a)^3(y) ?

The solution to expand (1-y/a)^3(y) is (y(a^3-3ya^2-y^3+3y^2a))/(a^3)

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expand (1-y/a)^3(y)

expand

(1 - \frac{y}{a})^{3} (y)

\frac{y ( a ^{3} - 3 y a ^{2} - y ^{3} + 3 y ^{2} a )}{a ^{3}}

Solution steps

(1 - \frac{y}{a})^{3} (y)

Apply rule:

(a) = a

(y) = y

= (1 - \frac{y}{a})^{3} y

= y (1 - \frac{y}{a})^{3}

Expand

(1 - \frac{y}{a})^{3} : \frac{a ^{3} - 3 y a ^{2} - y ^{3} + 3 y ^{2} a}{a ^{3}}

= y \frac{a ^{3} - 3 y a ^{2} - y ^{3} + 3 y ^{2} a}{a ^{3}}

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{y ( a ^{3} - 3 y a ^{2} - y ^{3} + 3 y ^{2} a )}{a ^{3}}

4 (2 x y + \frac{d}{d x} ((y) x^{2}))

(x^{2} - \frac{1}{x})^{9}

(6 - x) \cdot (4 x^{2} - 2)

(6 - 2 i)^{4}

\frac{x + 3}{y ( z + 5 )}

What is expand (1-y/a)^3(y) ?
The solution to expand (1-y/a)^3(y) is (y(a^3-3ya^2-y^3+3y^2a))/(a^3)