What is expand (1+(2x)/y)^3 ?

The solution to expand (1+(2x)/y)^3 is (y^3+6xy^2+8x^3+12x^2y)/(y^3)

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expand (1+(2x)/y)^3

expand

(1 + \frac{2 x}{y})^{3}

\frac{y ^{3} + 6 x y ^{2} + 8 x ^{3} + 12 x ^{2} y}{y ^{3}}

Solution steps

(1 + \frac{2 x}{y})^{3}

Apply Perfect Cube Formula:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

(1 + \frac{2 x}{y})^{3} = 1^{3} + 3 \cdot 1^{2} \cdot \frac{2 x}{y} + 3 \cdot 1 \cdot (\frac{2 x}{y})^{2} + (\frac{2 x}{y})^{3}

= 1^{3} + 3 \cdot 1^{2} \cdot \frac{2 x}{y} + 3 \cdot 1 \cdot (\frac{2 x}{y})^{2} + (\frac{2 x}{y})^{3}

Simplify

1^{3} + 3 \cdot 1^{2} \cdot \frac{2 x}{y} + 3 \cdot 1 \cdot (\frac{2 x}{y})^{2} + (\frac{2 x}{y})^{3} : \frac{y ^{3} + 6 x y ^{2} + 8 x ^{3} + 12 x ^{2} y}{y ^{3}}

= \frac{y ^{3} + 6 x y ^{2} + 8 x ^{3} + 12 x ^{2} y}{y ^{3}}

3 (t + Δ t)^{2} (- sin (Δ t) + cos (Δ t))

\frac{1 - 2 x}{( x + 1 ) ( x + 2 )}

(e^{2 x} - e^{- 2 x})^{2}

\frac{( ( n + 1 ) ^{2} ( 2 n ^{2} + 2 n - 1 ) )}{n ^{4}}

\frac{6 ( P - u w )}{L ( 4 P - 3 u w )}

What is expand (1+(2x)/y)^3 ?
The solution to expand (1+(2x)/y)^3 is (y^3+6xy^2+8x^3+12x^2y)/(y^3)