What is expand (ez-1)(z^2-2zcos(2k)+1) ?

The solution to expand (ez-1)(z^2-2zcos(2k)+1) is ez^3-2ez^2cos(2k)+ez-z^2+2zcos(2k)-1

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expand (ez-1)(z^2-2zcos(2k)+1)

expand

(ez - 1) (z^{2} - 2 z cos (2 k) + 1)

e z^{3} - 2 e z^{2} cos (2 k) + ez - z^{2} + 2 z cos (2 k) - 1

Solution steps

(ez - 1) (z^{2} - 2 z cos (2 k) + 1)

Distribute parentheses

= ez z^{2} + ez (- 2 z cos (2 k)) + ez \cdot 1 + (- 1) z^{2} + (- 1) (- 2 z cos (2 k)) + (- 1) \cdot 1

Apply minus-plus rules

+ (- a) = - a, (- a) (- b) = ab

= e z^{2} z - 2 ezz cos (2 k) + 1 ez - 1 \cdot z^{2} + 1 \cdot 2 z cos (2 k) - 1 \cdot 1

Simplify

e z^{2} z - 2 ezz cos (2 k) + 1 ez - 1 \cdot z^{2} + 1 \cdot 2 z cos (2 k) - 1 \cdot 1 : e z^{3} - 2 e z^{2} cos (2 k) + ez - z^{2} + 2 z cos (2 k) - 1

= e z^{3} - 2 e z^{2} cos (2 k) + ez - z^{2} + 2 z cos (2 k) - 1

- \frac{2}{5 ( 3 s + 1 )}

\frac{a ^{2} b c}{2 ( a ^{2} + b ^{2} )}

\frac{1}{( 3 x + 1 ) ^{3}}

\frac{x ( x + 6 )}{( x - 7 ) ( x + 1 )}

\frac{( 7 ( 1 - cos ( θ ) ) ^{2} )}{2}

What is expand (ez-1)(z^2-2zcos(2k)+1) ?
The solution to expand (ez-1)(z^2-2zcos(2k)+1) is ez^3-2ez^2cos(2k)+ez-z^2+2zcos(2k)-1