What is (x^2+x+1)^2+3x(x^2+x+1)+2x^2 ?

The solution to (x^2+x+1)^2+3x(x^2+x+1)+2x^2 is x^4+5x^3+8x^2+5x+1

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simplify (x^2+x+1)^2+3x(x^2+x+1)+2x^2

simplify

(x^{2} + x + 1)^{2} + 3 x (x^{2} + x + 1) + 2 x^{2}

x^{4} + 5 x^{3} + 8 x^{2} + 5 x + 1

Solution steps

(x^{2} + x + 1)^{2} + 3 x (x^{2} + x + 1) + 2 x^{2}

Expand

(x^{2} + x + 1)^{2} : x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1

= x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1 + 3 x (x^{2} + x + 1) + 2 x^{2}

Expand

3 x (x^{2} + x + 1) : 3 x^{3} + 3 x^{2} + 3 x

= x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1 + 3 x^{3} + 3 x^{2} + 3 x + 2 x^{2}

Group like terms

= x^{4} + 2 x^{3} + 3 x^{3} + 3 x^{2} + 3 x^{2} + 2 x^{2} + 2 x + 3 x + 1

Add similar elements:

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

= x^{4} + 5 x^{3} + 3 x^{2} + 3 x^{2} + 2 x^{2} + 2 x + 3 x + 1

Add similar elements:

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

= x^{4} + 5 x^{3} + 8 x^{2} + 2 x + 3 x + 1

Add similar elements:

2 x + 3 x = 5 x

= x^{4} + 5 x^{3} + 8 x^{2} + 5 x + 1

(\frac{1}{3 \cdot x ^{4} \cdot y ^{- 3}})^{2}

d [\frac{10}{x} - 4 x + 3 x^{0}]

x \cdot y^{2} - 10 x y + 21 x

n^{23} + n^{25} + n^{22}

t^{3} + t^{- 3}

What is (x^2+x+1)^2+3x(x^2+x+1)+2x^2 ?
The solution to (x^2+x+1)^2+3x(x^2+x+1)+2x^2 is x^4+5x^3+8x^2+5x+1