Smplizy: $$ x(x+1)+(x+1)(x+2) $$

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Calculate or simplify the expression $$ x(x+1)+(x+1)(x+2) $$.
Simplify the expression by following steps:
- step0: Solution:
  $$x\left(x+1\right)+\left(x+1\right)\left(x+2\right)$$
- step1: Expand the expression:
  $$x^{2}+x+\left(x+1\right)\left(x+2\right)$$
- step2: Expand the expression:
  $$x^{2}+x+x^{2}+3x+2$$
- step3: Add the terms:
  $$2x^{2}+4x+2$$
The simplified form of the expression $$ x(x+1)+(x+1)(x+2) $$ is $$ 2x^2 + 4x + 2 $$.
$$ 2x^2 + 4x + 2 $$

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