What is expand (1+(2t)/n)^3 ?

The solution to expand (1+(2t)/n)^3 is (n^3+6tn^2+8t^3+12nt^2)/(n^3)

Popular >

expand (1+(2t)/n)^3

expand

(1 + \frac{2 t}{n})^{3}

\frac{n ^{3} + 6 t n ^{2} + 8 t ^{3} + 12 n t ^{2}}{n ^{3}}

Solution steps

(1 + \frac{2 t}{n})^{3}

Apply Perfect Cube Formula:

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

(1 + \frac{2 t}{n})^{3} = 1^{3} + 3 \cdot 1^{2} \cdot \frac{2 t}{n} + 3 \cdot 1 \cdot (\frac{2 t}{n})^{2} + (\frac{2 t}{n})^{3}

= 1^{3} + 3 \cdot 1^{2} \cdot \frac{2 t}{n} + 3 \cdot 1 \cdot (\frac{2 t}{n})^{2} + (\frac{2 t}{n})^{3}

Simplify

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

= \frac{n ^{3} + 6 t n ^{2} + 8 t ^{3} + 12 n t ^{2}}{n ^{3}}

\frac{2 n - 2}{3 ( n + 1 )}

(7 - sec (x))^{2}

\frac{2 a s}{( s + a ) ( s ^{2} + a ^{2} ) ^{2}}

\frac{4 x ^{3} - 2 x y ^{3}}{y ^{2} ( 3 x ^{2} + 4 y )}

\frac{1}{( 3 - 4 x ) \cdot ( 3 + 4 x )}

What is expand (1+(2t)/n)^3 ?
The solution to expand (1+(2t)/n)^3 is (n^3+6tn^2+8t^3+12nt^2)/(n^3)