What is k(k+1)(2k+1)+6(k+1)^2 ?

The solution to k(k+1)(2k+1)+6(k+1)^2 is 2k^3+9k^2+13k+6

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simplify k(k+1)(2k+1)+6(k+1)^2

simplify

k (k + 1) (2 k + 1) + 6 (k + 1)^{2}

2 k^{3} + 9 k^{2} + 13 k + 6

Solution steps

k (k + 1) (2 k + 1) + 6 (k + 1)^{2}

Expand

k (k + 1) (2 k + 1) : 2 k^{3} + 3 k^{2} + k

= 2 k^{3} + 3 k^{2} + k + 6 (k + 1)^{2}

Expand

6 (k + 1)^{2} : 6 k^{2} + 12 k + 6

= 2 k^{3} + 3 k^{2} + k + 6 k^{2} + 12 k + 6

Group like terms

= 2 k^{3} + 3 k^{2} + 6 k^{2} + k + 12 k + 6

Add similar elements:

3 k^{2} + 6 k^{2} = 9 k^{2}

= 2 k^{3} + 9 k^{2} + k + 12 k + 6

Add similar elements:

k + 12 k = 13 k

= 2 k^{3} + 9 k^{2} + 13 k + 6

3 6^{4}

\frac{x ^{4}}{8} + \frac{1}{4 x ^{2}}

lo g_{3} (12) + lo g_{3} (5) + 5 lo g_{3} (7)

5 m (2 m)^{0} (2 n)^{3}

- 8 \cdot (- 1)

What is k(k+1)(2k+1)+6(k+1)^2 ?
The solution to k(k+1)(2k+1)+6(k+1)^2 is 2k^3+9k^2+13k+6