What is expand ((2n^3)/6+(3n^2)/6+n/6)^2 ?

The solution to expand ((2n^3)/6+(3n^2)/6+n/6)^2 is (n^6+n^4)/9+(n^5)/3+(n^4)/4+(n^3)/6+(n^2)/(36)

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expand ((2n^3)/6+(3n^2)/6+n/6)^2

expand

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2}

\frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

Solution steps

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})^{2} = (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}) (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})

= (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6}) (\frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} + \frac{n}{6})

Distribute parentheses

= \frac{2 n ^{3}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{n}{6} + \frac{3 n ^{2}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{n}{6} + \frac{n}{6} \cdot \frac{2 n ^{3}}{6} + \frac{n}{6} \cdot \frac{3 n ^{2}}{6} + \frac{n}{6} \cdot \frac{n}{6}

Simplify

\frac{2 n ^{3}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{2 n ^{3}}{6} \cdot \frac{n}{6} + \frac{3 n ^{2}}{6} \cdot \frac{2 n ^{3}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{3 n ^{2}}{6} + \frac{3 n ^{2}}{6} \cdot \frac{n}{6} + \frac{n}{6} \cdot \frac{2 n ^{3}}{6} + \frac{n}{6} \cdot \frac{3 n ^{2}}{6} + \frac{n}{6} \cdot \frac{n}{6} : \frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

= \frac{n ^{6} + n ^{4}}{9} + \frac{n ^{5}}{3} + \frac{n ^{4}}{4} + \frac{n ^{3}}{6} + \frac{n ^{2}}{36}

\frac{2 ( 7 - 4 )}{3}

(\frac{b}{a} (x - z) + y + c)^{3}

l {e^{4 t} (t - cos (t))}

(1 + x)^{2}

- \frac{100}{( x + 1 ) ^{2}}

What is expand ((2n^3)/6+(3n^2)/6+n/6)^2 ?
The solution to expand ((2n^3)/6+(3n^2)/6+n/6)^2 is (n^6+n^4)/9+(n^5)/3+(n^4)/4+(n^3)/6+(n^2)/(36)