What is expand x(1-x-x^3+x^4)^2 ?

The solution to expand x(1-x-x^3+x^4)^2 is x^9-2x^8+x^7-2x^6+4x^5-2x^4+x^3-2x^2+x

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expand x(1-x-x^3+x^4)^2

expand

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

x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

Solution steps

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

(1 - x - x^{3} + x^{4})^{2} = x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} - 2 x + 1

= x (x^{8} - 2 x^{7} + x^{6} - 2 x^{5} + 4 x^{4} - 2 x^{3} + x^{2} - 2 x + 1)

Distribute parentheses

= x x^{8} + x (- 2 x^{7}) + x x^{6} + x (- 2 x^{5}) + x \cdot 4 x^{4} + x (- 2 x^{3}) + x x^{2} + x (- 2 x) + x \cdot 1

Apply minus-plus rules

+ (- a) = - a

= x^{8} x - 2 x^{7} x + x^{6} x - 2 x^{5} x + 4 x^{4} x - 2 x^{3} x + x^{2} x - 2 xx + 1 \cdot x

Simplify

x^{8} x - 2 x^{7} x + x^{6} x - 2 x^{5} x + 4 x^{4} x - 2 x^{3} x + x^{2} x - 2 xx + 1 \cdot x : x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

= x^{9} - 2 x^{8} + x^{7} - 2 x^{6} + 4 x^{5} - 2 x^{4} + x^{3} - 2 x^{2} + x

cos (3 t) U (t - \frac{7 π}{2})

V (2, - 3) F (2, - 4)

(4 m + 2 n = 70,) (- 3 m + 4 n = 30)

\frac{1}{( x + n + 1 ) ^{2}}

3 (403)

What is expand x(1-x-x^3+x^4)^2 ?
The solution to expand x(1-x-x^3+x^4)^2 is x^9-2x^8+x^7-2x^6+4x^5-2x^4+x^3-2x^2+x