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

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

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expand x(x^2+x+1)^2

expand

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

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

Solution steps

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

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

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

Distribute parentheses

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

= x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x

Simplify

x^{4} x + 2 x^{3} x + 3 x^{2} x + 2 xx + 1 \cdot x : x^{5} + 2 x^{4} + 3 x^{3} + 2 x^{2} + x

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

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