What is ((n^2(n+1)^2))/4-((n(n+1)))/2 ?

The solution to ((n^2(n+1)^2))/4-((n(n+1)))/2 is (n^4+2n^3-n^2-2n)/4

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simplify ((n^2(n+1)^2))/4-((n(n+1)))/2

simplify

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

\frac{n ^{4} + 2 n ^{3} - n ^{2} - 2 n}{4}

Solution steps

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

Least Common Multiplier of

4, 2 : 4

Adjust Fractions based on the LCM

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

Apply the fraction rule:

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

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

Simplify

n^{2} (n + 1)^{2} - n (n + 1) \cdot 2 : n^{4} + 2 n^{3} - n^{2} - 2 n

= \frac{n ^{4} + 2 n ^{3} - n ^{2} - 2 n}{4}

(x - 2)^{2} = 100

2 x \geq 8

x^{2} - 2 x = 12

- \frac{1.2 ( 5 )}{( 0.01 ( 5 ) ^{2} + 1 ) ^{2}}

2 (3 z - 1) = 46

What is ((n^2(n+1)^2))/4-((n(n+1)))/2 ?
The solution to ((n^2(n+1)^2))/4-((n(n+1)))/2 is (n^4+2n^3-n^2-2n)/4