### Related

##### expandwrt-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

E_gu: n_g*E;

E_gw: (1-n_g)*E;

E_su: n_s*E_gw;

Calculate

##### expandwrt-solve-subst

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

f:(4*a+b*a);

expandwrt(f,a);

Calculate

##### expandwrt-ratsimp-subst

L1:alfa*L0;

L2:L0/2-L1;

M(x):=q*L0/2*x-q*x*x/2;

Calculate

? expandwrt;

Calculate

##### expandwrt

expandwrt((1-a) * (1+...

expandwrt(2 * (1-a*z)...

expandwrt((1-a) * (1-...

Calculate

##### expandwrt-integrate-sqrt

myDot(f,g):= integrat...

myNorm(v) := sqrt(myD...

proj(w,v) := (myDot(w...

Calculate

##### expandwrt-ratsimp

r1:(x+y+1/(x+y));

r2:ratsimp(r1,(y+x));

expandwrt(r2);

Calculate

E_gu: n_g*E;

E_gw: (1-n_g)*E;

E_su: n_s*E_gw;

Calculate

### expandwrt

Run Example
```(%i1)expandwrt((1-a) * (1+z), z);
(%o1)                          (1 - a) z - a + 1
(%i2) expandwrt(2 * (1-a*z), z);
(%o2)                              2 - 2 a z
(%i3) expandwrt((1-a) * (1-z), z);
(%o3)                         - (1 - a) z - a + 1
(%i4) expandwrt(2 * (1+a*z), z);
(%o4)                              2 a z + 2
(%i5) H4: G*(z-1)*(z+1) / ((z-%i*r)*(z+%i*r));
(z - 1) (z + 1) G
(%o5)                        ---------------------
(z - %i r) (z + %i r)
(%i6) ```
Run Example
```display2d:false;

(%o1) false
(%i2)
x1: a2*z1^2 + b2*z1 +c2;

(%o2) a2*z1^2+b2*z1+c2
(%i3)
y1: a1*z1^2 + b1*z1 +c1;

(%o3) a1*z1^2+b1*z1+c1
(%i4)
e: A * x1^2 - B1 * x1  - x^2 * y1 + x * y1 * x1  + C1 = 0;

(%o4) C1-(a2*z1^2+b2*z1+c2)*B1+(a2*z1^2+b2*z1+c2)^2*A
+x*(a1*z1^2+b1*z1+c1)*(a2*z1^2+b2*z1+c2)-x^2*(a1*z1^2+b1*z1+c1)
= 0
(%i5)
expandwrt(expand(e), z1);

(%o5) C1-a2*z1^2*B1-b2*z1*B1-c2*B1+a2^2*z1^4*A+2*a2*b2*z1^3*A+2*a2*c2*z1^2*A
+b2^2*z1^2*A+2*b2*c2*z1*A+c2^2*A+a1*a2*x*z1^4+a1*b2*x*z1^3
+a2*b1*x*z1^3-a1*x^2*z1^2+a1*c2*x*z1^2+a2*c1*x*z1^2+b1*b2*x*z1^2
-b1*x^2*z1+b1*c2*x*z1+b2*c1*x*z1-c1*x^2+c1*c2*x
= 0
(%i6)
```
Run Example
```myDot(f,g):= integrate(f*g,x,-Pi,Pi);
(%o1)             myDot(f, g) := integrate(f g, x, - Pi, Pi)
(%i2) myNorm(v) := sqrt(myDot(v,v));
(%o2)                   myNorm(v) := sqrt(myDot(v, v))
(%i3) proj(w,v) := (myDot(w,v)/myDot(v,v)) * v;
myDot(w, v)
(%o3)                     proj(w, v) := ----------- v
myDot(v, v)
(%i4) u : [1, x, x^2, x^3];
2   3
(%o4)                           [1, x, x , x ]
(%i5) proj(u,1);
2
Pi
(%o5)                           [1, 0, ---, 0]
3
(%i6) u[2] : x - proj(x,1);
(%o6)                                  x
(%i7) u[3] : x^2 - proj(x^2,1) - proj(x^2,x);
2
2   Pi
(%o7)                              x  - ---
3
(%i8) u[4] : x^3 - proj(x^3,1) - proj(x^3,x) - proj(x^3,x^2);
2
3   3 Pi  x
(%o8)                            x  - -------
5
(%i9) q : expandwrt(u/myNorm(u),x);
2
1            sqrt(3) x    3 sqrt(5) x       sqrt(5)
(%o9) [----------------, -------------, ------------ - -------------,
sqrt(2) sqrt(Pi)            3/2    3/2   5/2     3/2
sqrt(2) Pi      2    Pi       2    sqrt(Pi)
3
5 sqrt(7) x    3 sqrt(7) x
------------ - -----------]
3/2   7/2     3/2   3/2
2    Pi       2    Pi
(%i10) ```

### Related Help

Help for Expandwrt