How do you simplify $2 {(k + 1)}^{3} + 3 {(k + 1)}^{2} + k + 1$ $2(k+1)^3+3(k+1)^2+k+1$ ?

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How do you simplify $2 {(k + 1)}^{3} + 3 {(k + 1)}^{2} + k + 1$ $2(k+1)^3+3(k+1)^2+k+1$ ?

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Answer 1 · 2016-06-19T10:39:18

$(k + 1) (2 k + 3) (k + 2)$ $(k+1)(2k+3)(k+2)$

Explanation:

Let $k + 1 = x$ $k+1=x$
So $2 {(k + 1)}^{3} + 3 {(k + 1)}^{2} + (k + 1)$ $2(k+1)^3+3(k+1)^2+(k+1)$
= $2 x^{3} + 3 x^{2} + x$ $2x^3+3x^2+x$
= $x (2 x^{2} + 3 x + 1)$ $x(2x^2+3x+1)$
Use {cross product method}
It ca be factored as
= $x (2 x + 1) (x + 1)$ $x(2x+1)(x+1)$
Back!!
= $(k + 1) (2 k + 3) (k + 2)$ $(k+1)(2k+3)(k+2)$

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How do you simplify $2 {(k + 1)}^{3} + 3 {(k + 1)}^{2} + k + 1$ $2(k+1)^3+3(k+1)^2+k+1$ ?

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