What is (x^2+x+2)(x^2+4x+2)+2x^2 ?

The solution to (x^2+x+2)(x^2+4x+2)+2x^2 is x^4+5x^3+10x^2+10x+4

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simplify (x^2+x+2)(x^2+4x+2)+2x^2

simplify

(x^{2} + x + 2) (x^{2} + 4 x + 2) + 2 x^{2}

x^{4} + 5 x^{3} + 10 x^{2} + 10 x + 4

Solution steps

(x^{2} + x + 2) (x^{2} + 4 x + 2) + 2 x^{2}

Expand

(x^{2} + x + 2) (x^{2} + 4 x + 2) : x^{4} + 5 x^{3} + 8 x^{2} + 10 x + 4

= x^{4} + 5 x^{3} + 8 x^{2} + 10 x + 4 + 2 x^{2}

Group like terms

= x^{4} + 5 x^{3} + 8 x^{2} + 2 x^{2} + 10 x + 4

Add similar elements:

8 x^{2} + 2 x^{2} = 10 x^{2}

= x^{4} + 5 x^{3} + 10 x^{2} + 10 x + 4

l - 1 [2 s^{4} - 2 s^{3} + 6 s^{2} - 8 s + 8 (s^{5} + 4 s^{3})]

\frac{1}{2} - \frac{x ^{2}}{50}

(2 n + 5)^{3}

(x + (\frac{9 y}{2}) - 2 x - 2 - 5 y - (\frac{5}{2}) + 28)^{2}

27 + 27 x + 9 x^{2} + x^{3}

What is (x^2+x+2)(x^2+4x+2)+2x^2 ?
The solution to (x^2+x+2)(x^2+4x+2)+2x^2 is x^4+5x^3+10x^2+10x+4