What is expand (1+x+x^2)^5 ?

The solution to expand (1+x+x^2)^5 is x^{10}+5x^9+15x^8+30x^7+45x^6+51x^5+45x^4+30x^3+15x^2+5x+1

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expand (1+x+x^2)^5

expand

(1 + x + x^{2})^{5}

x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

Solution steps

(1 + x + x^{2})^{5}

(1 + x + x^{2})^{5} = (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2})

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

Expand

(1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) (1 + x + x^{2}) : x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

= x^{10} + 5 x^{9} + 15 x^{8} + 30 x^{7} + 45 x^{6} + 51 x^{5} + 45 x^{4} + 30 x^{3} + 15 x^{2} + 5 x + 1

(1 + 6) (5 - 7)

\frac{70}{( x + 1 ) ( x ^{2} + 9 ) ^{2}}

\frac{1}{( s + 1 ) ( s ^{2} - 2 s + 4 )}

(x - 32) (x + 32)

(x - x^{2})^{2}

What is expand (1+x+x^2)^5 ?
The solution to expand (1+x+x^2)^5 is x^{10}+5x^9+15x^8+30x^7+45x^6+51x^5+45x^4+30x^3+15x^2+5x+1