What is (x+1)2+x(x+2)(x+2)2+x^2 ?

The solution to (x+1)2+x(x+2)(x+2)2+x^2 is 2x^3+9x^2+10x+2

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simplify (x+1)2+x(x+2)(x+2)2+x^2

simplify

(x + 1) 2 + x (x + 2) (x + 2) 2 + x^{2}

2 x^{3} + 9 x^{2} + 10 x + 2

Solution steps

(x + 1) \cdot 2 + x (x + 2) (x + 2) \cdot 2 + x^{2}

Simplify

x (x + 2) (x + 2) \cdot 2 : 2 x (x + 2)^{2}

= (x + 1) \cdot 2 + 2 x (x + 2)^{2} + x^{2}

= 2 (x + 1) + 2 x (x + 2)^{2} + x^{2}

Expand

2 (x + 1) : 2 x + 2

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

Expand

2 x (x + 2)^{2} : 2 x^{3} + 8 x^{2} + 8 x

= 2 x + 2 + 2 x^{3} + 8 x^{2} + 8 x + x^{2}

Group like terms

= 2 x^{3} + 8 x^{2} + x^{2} + 2 x + 8 x + 2

Add similar elements:

8 x^{2} + x^{2} = 9 x^{2}

= 2 x^{3} + 9 x^{2} + 2 x + 8 x + 2

Add similar elements:

2 x + 8 x = 10 x

= 2 x^{3} + 9 x^{2} + 10 x + 2

0.1 20000

1 0^{l o g_{10} (9)}

- \frac{16}{25}

6 \div 6

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What is (x+1)2+x(x+2)(x+2)2+x^2 ?
The solution to (x+1)2+x(x+2)(x+2)2+x^2 is 2x^3+9x^2+10x+2