展开 (xy(x,z(x))+z'(x))(xz'(x)+y(x,z(x))z(x))

解答

展开

(x y (x, z (x)) + z^{'}) (x z^{'} + y (x, z (x)) z (x))

xx y (, x (x) z) z' + x (x) zy (, x (x) z) y (, x (x) z) + x z' z' + (x) zz' y (, x (x) z)

求解步骤

(x y (x, z (x)) + z^{'}) (x z^{'} + y (x, z (x)) z (x))

= (x y (, x (x) z) + z^{^{'}}) (x z^{^{'}} + (x) zy (, x (x) z))

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = x y (x, z (x)), b = z^{'}, c = x z^{'}, d = y (x, z (x)) z (x)

= x y (x, z (x)) x z^{^{'}} + x y (x, z (x)) y (x, z (x)) z (x) + z^{^{'}} x z^{^{'}} + z^{^{'}} y (x, z (x)) z (x)

= xx y (, x (x) z) z^{^{'}} + x (x) zy (, x (x) z) y (, x (x) z) + x z^{^{'}} z^{^{'}} + (x) z z^{^{'}} y (, x (x) z)

e x p an d \frac{( x + 3 ) ( x - 6 )}{x - 2}

e x p an d \frac{3 - x}{( x + 1 ) ( x - 1 )}

e x p an d A (- 2, - 5) y B (4, - 3)

e x p an d \frac{2 s ^{2} + 10 s}{( s ^{2} - 2 s + 5 ) ( s + 1 )}

e x p an d D x (e^{4} + cos (3 x))