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

The solution to expand (1+x-2x^2)^5 is -32x^{10}+80x^9-120x^7+30x^6+81x^5-15x^4-30x^3+5x+1

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

expand

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

- 32 x^{10} + 80 x^{9} - 120 x^{7} + 30 x^{6} + 81 x^{5} - 15 x^{4} - 30 x^{3} + 5 x + 1

Solution steps

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

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

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

Expand

(1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) (1 + x - 2 x^{2}) : - 32 x^{10} + 80 x^{9} - 120 x^{7} + 30 x^{6} + 81 x^{5} - 15 x^{4} - 30 x^{3} + 5 x + 1

= - 32 x^{10} + 80 x^{9} - 120 x^{7} + 30 x^{6} + 81 x^{5} - 15 x^{4} - 30 x^{3} + 5 x + 1

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

(2 x + \frac{y}{4})^{16}

(100 - e^{2}) \cdot 200

- \frac{2 x + h}{x ^{2} ( x + h ) ^{2}}

x d y + (x - y) d x

What is expand (1+x-2x^2)^5 ?
The solution to expand (1+x-2x^2)^5 is -32x^{10}+80x^9-120x^7+30x^6+81x^5-15x^4-30x^3+5x+1