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

The solution to expand (1+2x-x^2)^5 is -x^{10}+10x^9-35x^8+40x^7+30x^6-68x^5-30x^4+40x^3+35x^2+10x+1

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

expand

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

- x^{10} + 10 x^{9} - 35 x^{8} + 40 x^{7} + 30 x^{6} - 68 x^{5} - 30 x^{4} + 40 x^{3} + 35 x^{2} + 10 x + 1

Solution steps

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

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

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

Expand

(1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) (1 + 2 x - x^{2}) : - x^{10} + 10 x^{9} - 35 x^{8} + 40 x^{7} + 30 x^{6} - 68 x^{5} - 30 x^{4} + 40 x^{3} + 35 x^{2} + 10 x + 1

= - x^{10} + 10 x^{9} - 35 x^{8} + 40 x^{7} + 30 x^{6} - 68 x^{5} - 30 x^{4} + 40 x^{3} + 35 x^{2} + 10 x + 1

f (n) = (- 1)^{n + 1} (1 + \frac{1}{n ^{2}})

(z - \frac{1}{z})^{2}

\frac{k ( 2 k + 1 ) ( 4 k + 1 )}{3} + (2 (k + 1))^{2}

(x - \frac{5}{4})^{2} + 3

(x sin (θ) + y cos (θ))^{2}

What is expand (1+2x-x^2)^5 ?
The solution to expand (1+2x-x^2)^5 is -x^{10}+10x^9-35x^8+40x^7+30x^6-68x^5-30x^4+40x^3+35x^2+10x+1