What is expand (n+1)(n/2)(n+1) ?

The solution to expand (n+1)(n/2)(n+1) is (n^3+n)/2+n^2

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expand (n+1)(n/2)(n+1)

expand

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

\frac{n ^{3} + n}{2} + n^{2}

Solution steps

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

Apply rule:

(a) = a

(\frac{n}{2}) = \frac{n}{2}

= (n + 1) \frac{n}{2} (n + 1)

= \frac{n}{2} (n + 1) (n + 1)

Apply FOIL method

(n + 1) (n + 1) : n^{2} + 2 n + 1

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

Apply the distributive law:

m (a + b + c) = ma + mb + m c

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

= \frac{n}{2} n^{2} + \frac{n}{2} \cdot 2 n + \frac{n}{2} \cdot 1

Simplify

\frac{n}{2} n^{2} + \frac{n}{2} \cdot 2 n + \frac{n}{2} \cdot 1 : \frac{n ^{3} + n}{2} + n^{2}

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

(s + p_{o}) (s + p_{1}) (s + p_{2})

(x - y) \frac{d}{d y} (x y + 2)

\frac{2 ( 2 + 10 )}{3}

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

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

What is expand (n+1)(n/2)(n+1) ?
The solution to expand (n+1)(n/2)(n+1) is (n^3+n)/2+n^2