What is 2(k+1)^3+3(k+1)^2+7(k+1) ?

The solution to 2(k+1)^3+3(k+1)^2+7(k+1) is 2k^3+9k^2+19k+12

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simplify 2(k+1)^3+3(k+1)^2+7(k+1)

simplify

2 (k + 1)^{3} + 3 (k + 1)^{2} + 7 (k + 1)

2 k^{3} + 9 k^{2} + 19 k + 12

Solution steps

2 (k + 1)^{3} + 3 (k + 1)^{2} + 7 (k + 1)

Expand

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

= 2 k^{3} + 6 k^{2} + 6 k + 2 + 3 (k + 1)^{2} + 7 (k + 1)

Expand

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

= 2 k^{3} + 6 k^{2} + 6 k + 2 + 3 k^{2} + 6 k + 3 + 7 (k + 1)

Expand

7 (k + 1) : 7 k + 7

= 2 k^{3} + 6 k^{2} + 6 k + 2 + 3 k^{2} + 6 k + 3 + 7 k + 7

Group like terms

= 2 k^{3} + 6 k^{2} + 3 k^{2} + 6 k + 6 k + 7 k + 2 + 3 + 7

Add similar elements:

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

= 2 k^{3} + 9 k^{2} + 6 k + 6 k + 7 k + 2 + 3 + 7

Add similar elements:

6 k + 6 k + 7 k = 19 k

= 2 k^{3} + 9 k^{2} + 19 k + 2 + 3 + 7

Add the numbers:

2 + 3 + 7 = 12

= 2 k^{3} + 9 k^{2} + 19 k + 12

2 \frac{3}{8} - 1 \frac{3}{4}

\frac{4 x ^{2} + 4 x}{x ^{2} + 5 x + 4}

(- 2 i)^{2}

(- 3)^{8}

(- 3 + 8 i) (- 3 - 8 i)

What is 2(k+1)^3+3(k+1)^2+7(k+1) ?
The solution to 2(k+1)^3+3(k+1)^2+7(k+1) is 2k^3+9k^2+19k+12