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

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

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

expand

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

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

Solution steps

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

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

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

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

Distribute parentheses

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

Simplify

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

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

\frac{- 24 x ^{7} y ^{3}}{8 x ^{9} y}

(3 b + c - d) + (2 b + 3 c - 4 d)

\frac{x - 9}{x ^{2} - 81}

\frac{44 !}{2 !}

1 8^{5}

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