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@acer In the following case factor(expan...

ignacios 10
March 10 2024
0 0

@acer In the following case factor(expand(combine(expression), trig)) does not work, but simplify(factor(expand(combine(expression), trig))) does work:


 

> 

expr3 := (8*m^2*r^2*(3*a^2*cos(theta)^2-r^2)^2*(r^2+a^2*cos(theta)^2)^2*(a^2-2*m*r+r^2)^5+8*(a^2*cos(theta)^2-3*a^2-2*r^2)^2*(3*a^2*cos(theta)^2-r^2)^2*m^2*r^2*(a^2-2*m*r+r^2)^5-144*(3*a^2*cos(theta)^2-r^2)^2*a^2*m^2*r^2*sin(theta)^2*(a^2+r^2)*(a^2-2*m*r+r^2)^5-8*sin(theta)*(a^2*cos(theta)^2-3*r^2)^2*cos(theta)*m^2*a^2*cot(theta)*(r^2+a^2*cos(theta)^2)^2*(a^2-2*m*r+r^2)^5-8*sin(theta)*(cos(theta)^2*(cos(theta)^2-3)*a^10+2*cos(theta)^2*(7-3*cos(theta)^2)*a^8*m*r+(3*cos(theta)^4-14*cos(theta)^2+9)*a^8*r^2+4*cos(theta)^2*(-5+3*cos(theta)^2)*a^6*m^2*r^2+(6*(-7+2*cos(theta)^2))*sin(theta)^2*a^6*m*r^3+(3*(cos(theta)^4-8*cos(theta)^2+11))*a^6*r^4+8*cos(theta)^2*sin(theta)^2*a^4*m^3*r^3+(4*(3*cos(theta)^4-16*cos(theta)^2+15))*a^4*m^2*r^4+(6*(-cos(theta)^4+11*cos(theta)^2-18))*a^4*m*r^5+(cos(theta)^4-18*cos(theta)^2+45)*a^4*r^6-24*sin(theta)^2*a^2*m^3*r^5+(4*(21-11*cos(theta)^2))*a^2*m^2*r^6+(2*(-45+13*cos(theta)^2))*a^2*m*r^7+(-5*cos(theta)^2+27)*a^2*r^8+24*m^2*r^8-24*m*r^9+6*r^10)*cos(theta)*m^2*a^2*cot(theta)*(16*a^6*cos(theta)^2*m*r-28*cos(theta)^2*a^4*m^2*r^2+40*cos(theta)^2*a^4*m*r^3+16*a^2*cos(theta)^2*m^3*r^3-36*a^2*cos(theta)^2*m^2*r^4+24*a^2*cos(theta)^2*m*r^5+cos(theta)^4*a^4*r^4+21*a^2*r^6-48*m^3*r^5+72*m^2*r^6-36*m*r^7-3*a^8*cos(theta)^2+24*a^4*r^4+a^8*cos(theta)^4-84*a^2*m*r^5+84*a^2*m^2*r^4+9*sin(theta)^2*a^6*r^2-13*cos(theta)^2*a^4*r^4-48*a^4*m*r^3-5*a^2*cos(theta)^2*r^6-4*cos(theta)^4*a^6*m*r+4*cos(theta)^4*a^4*m^2*r^2+6*r^8-4*cos(theta)^4*a^4*m*r^3-2*cos(theta)^2*sin(theta)^2*a^6*r^2)*(r^2+a^2*cos(theta)^2)^4/(cos(theta)^8*a^8+4*cos(theta)^6*a^6*r^2+6*cos(theta)^4*a^4*r^4+4*a^2*cos(theta)^2*r^6+r^8)+8*(2*a^2*cos(theta)^2-3*a^2-r^2)^2*(3*a^2*cos(theta)^2-r^2)^2*m^2*r^2*(a^2-2*m*r+r^2)^5-8*cot(theta)*(14*a^6*cos(theta)^2*m*r-20*cos(theta)^2*a^4*m^2*r^2+44*cos(theta)^2*a^4*m*r^3+8*a^2*cos(theta)^2*m^3*r^3-36*a^2*cos(theta)^2*m^2*r^4+30*a^2*cos(theta)^2*m*r^5+2*cos(theta)^4*a^4*r^4+15*a^2*r^6-24*m^3*r^5+36*m^2*r^6-18*m*r^7-3*a^8*cos(theta)^2+21*a^4*r^4+2*a^8*cos(theta)^4-60*a^2*m*r^5+60*a^2*m^2*r^4+9*sin(theta)^2*a^6*r^2-17*cos(theta)^2*a^4*r^4-42*a^4*m*r^3-7*a^2*cos(theta)^2*r^6-8*cos(theta)^4*a^6*m*r+8*cos(theta)^4*a^4*m^2*r^2+3*r^8-8*cos(theta)^4*a^4*m*r^3-4*cos(theta)^2*sin(theta)^2*a^6*r^2)*a^2*m^2*sin(theta)*(cos(theta)^2*(2*cos(theta)^2-3)*a^10+4*cos(theta)^2*(4-3*cos(theta)^2)*a^8*m*r+(6*cos(theta)^4-16*cos(theta)^2+9)*a^8*r^2+4*cos(theta)^2*(-7+6*cos(theta)^2)*a^6*m^2*r^2+(24*(-2+cos(theta)^2))*sin(theta)^2*a^6*m*r^3+(6*(cos(theta)^4-5*cos(theta)^2+5))*a^6*r^4+16*cos(theta)^2*sin(theta)^2*a^4*m^3*r^3+(4*(21+6*cos(theta)^4-26*cos(theta)^2))*a^4*m^2*r^4+(12*(-cos(theta)^4+8*cos(theta)^2-9))*a^4*m*r^5+(2*(cos(theta)^4-12*cos(theta)^2+18))*a^4*r^6-48*sin(theta)^2*a^2*m^3*r^5+(4*(24-19*cos(theta)^2))*a^2*m^2*r^6+(8*(-9+5*cos(theta)^2))*a^2*m*r^7+(-7*cos(theta)^2+18)*a^2*r^8+12*m^2*r^8-12*m*r^9+3*r^10)*cos(theta)*(r^2+a^2*cos(theta)^2)^4/(cos(theta)^8*a^8+4*cos(theta)^6*a^6*r^2+6*cos(theta)^4*a^4*r^4+4*a^2*cos(theta)^2*r^6+r^8)+8*sin(theta)^2*(9*sin(theta)^2*a^6*r^2-3*a^8*cos(theta)^2+16*a^6*cos(theta)^2*m*r-28*cos(theta)^2*a^4*m^2*r^2+32*cos(theta)^2*a^4*m*r^3-9*cos(theta)^2*a^4*r^4+16*a^2*cos(theta)^2*m^3*r^3-28*a^2*cos(theta)^2*m^2*r^4+16*a^2*cos(theta)^2*m*r^5-3*a^2*cos(theta)^2*r^6-48*a^4*m*r^3+27*a^4*r^4+84*a^2*m^2*r^4-96*a^2*m*r^5+27*a^2*r^6-48*m^3*r^5+84*m^2*r^6-48*m*r^7+9*r^8)*cos(theta)^2*a^4*m^2*(9*sin(theta)^2*a^6*r^2-3*a^8*cos(theta)^2+14*a^6*cos(theta)^2*m*r-20*cos(theta)^2*a^4*m^2*r^2+28*cos(theta)^2*a^4*m*r^3-9*cos(theta)^2*a^4*r^4+8*a^2*cos(theta)^2*m^3*r^3-20*a^2*cos(theta)^2*m^2*r^4+14*a^2*cos(theta)^2*m*r^5-3*a^2*cos(theta)^2*r^6-42*a^4*m*r^3+27*a^4*r^4+60*a^2*m^2*r^4-84*a^2*m*r^5+27*a^2*r^6-24*m^3*r^5+60*m^2*r^6-42*m*r^7+9*r^8)+8*sin(theta)^2*(3*a^8*cos(theta)^2-16*a^6*cos(theta)^2*m*r+28*cos(theta)^2*a^4*m^2*r^2-32*cos(theta)^2*a^4*m*r^3+9*cos(theta)^2*a^4*r^4-16*a^2*cos(theta)^2*m^3*r^3+28*a^2*cos(theta)^2*m^2*r^4-16*a^2*cos(theta)^2*m*r^5+3*a^2*cos(theta)^2*r^6-9*sin(theta)^2*a^6*r^2+48*a^4*m*r^3-27*a^4*r^4-84*a^2*m^2*r^4+96*a^2*m*r^5-27*a^2*r^6+48*m^3*r^5-84*m^2*r^6+48*m*r^7-9*r^8)*cos(theta)^2*a^4*m^2*(3*a^8*cos(theta)^2-14*a^6*cos(theta)^2*m*r+20*cos(theta)^2*a^4*m^2*r^2-28*cos(theta)^2*a^4*m*r^3+9*cos(theta)^2*a^4*r^4-8*a^2*cos(theta)^2*m^3*r^3+20*a^2*cos(theta)^2*m^2*r^4-14*a^2*cos(theta)^2*m*r^5+3*a^2*cos(theta)^2*r^6-9*sin(theta)^2*a^6*r^2+42*a^4*m*r^3-27*a^4*r^4-60*a^2*m^2*r^4+84*a^2*m*r^5-27*a^2*r^6+24*m^3*r^5-60*m^2*r^6+42*m*r^7-9*r^8))/((r^2+a^2*cos(theta)^2)^8*(a^2-2*m*r+r^2)^5)
> 

expr4 := 48*m^2*(-a^6*(a^2-2*m*r+r^2)*cos(theta)^6+(15*a^6*r^2-30*a^4*m*r^3)*cos(theta)^4-15*a^2*r^4*(sin(theta)^2*a^2-2*m*r+r^2)*cos(theta)^2+a^2*r^6-2*m*r^7+r^8)/((r^2+a^2*cos(theta)^2)^6*(a^2-2*m*r+r^2))
> 

simplify(expr3-expr4)

0

 (1)
> 

factor(expand(combine(expr3), trig))

-16*(3*cos(theta)^9*sin(theta)*cot(theta)*a^12-9*cos(theta)^7*sin(theta)*cot(theta)*a^12-18*cos(theta)^8*a^10*m*r+8*cos(theta)^8*a^8*m^2*r^2+36*cos(theta)^8*a^8*m*r^3+9*cos(theta)^5*sin(theta)*cot(theta)*a^12+18*cos(theta)^6*a^10*m*r-8*cos(theta)^6*a^8*m^2*r^2+126*cos(theta)^6*a^8*m*r^3-48*cos(theta)^6*a^6*m^2*r^4+180*cos(theta)^6*a^6*m*r^5-108*cos(theta)^4*a^8*m*r^3+48*cos(theta)^4*a^6*m^2*r^4-270*cos(theta)^4*a^6*m*r^5+72*cos(theta)^4*a^4*m^2*r^6-174*cos(theta)^4*a^4*m*r^7+162*cos(theta)^2*a^6*m*r^5-72*cos(theta)^2*a^4*m^2*r^6+162*cos(theta)^2*a^4*m*r^7-24*cos(theta)^2*a^2*m*r^9+48*cos(theta)^5*sin(theta)*cot(theta)*a^6*r^6-54*cos(theta)^3*sin(theta)*cot(theta)*a^10*r^2-189*cos(theta)^3*sin(theta)*cot(theta)*a^8*r^4-180*cos(theta)^3*sin(theta)*cot(theta)*a^6*r^6-45*cos(theta)^3*sin(theta)*cot(theta)*a^4*r^8+81*cos(theta)*sin(theta)*cot(theta)*a^8*r^4+162*cos(theta)*sin(theta)*cot(theta)*a^6*r^6+108*cos(theta)*sin(theta)*cot(theta)*a^4*r^8+27*cos(theta)*sin(theta)*cot(theta)*a^2*r^10+3*cos(theta)^9*sin(theta)*cot(theta)*a^10*r^2-30*cos(theta)^7*sin(theta)*cot(theta)*a^10*r^2-21*cos(theta)^7*sin(theta)*cot(theta)*a^8*r^4+72*cos(theta)^5*sin(theta)*cot(theta)*a^10*r^2+111*cos(theta)^5*sin(theta)*cot(theta)*a^8*r^4-6*cos(theta)^9*sin(theta)*cot(theta)*a^10*m*r+18*cos(theta)^7*sin(theta)*cot(theta)*a^10*m*r-8*cos(theta)^7*sin(theta)*cot(theta)*a^8*m^2*r^2+42*cos(theta)^7*sin(theta)*cot(theta)*a^8*m*r^3-18*cos(theta)^5*sin(theta)*cot(theta)*a^10*m*r+8*cos(theta)^5*sin(theta)*cot(theta)*a^8*m^2*r^2-126*cos(theta)^5*sin(theta)*cot(theta)*a^8*m*r^3+48*cos(theta)^5*sin(theta)*cot(theta)*a^6*m^2*r^4-96*cos(theta)^5*sin(theta)*cot(theta)*a^6*m*r^5+108*cos(theta)^3*sin(theta)*cot(theta)*a^8*m*r^3-48*cos(theta)^3*sin(theta)*cot(theta)*a^6*m^2*r^4+270*cos(theta)^3*sin(theta)*cot(theta)*a^6*m*r^5-72*cos(theta)^3*sin(theta)*cot(theta)*a^4*m^2*r^6+90*cos(theta)^3*sin(theta)*cot(theta)*a^4*m*r^7-162*cos(theta)*sin(theta)*cot(theta)*a^6*m*r^5+72*cos(theta)*sin(theta)*cot(theta)*a^4*m^2*r^6-162*cos(theta)*sin(theta)*cot(theta)*a^4*m*r^7-54*cos(theta)*sin(theta)*cot(theta)*a^2*m*r^9-3*a^2*r^10+6*m*r^11+9*cos(theta)^8*a^12-9*cos(theta)^6*a^12-9*cos(theta)^8*a^10*r^2-72*cos(theta)^6*a^10*r^2-153*cos(theta)^6*a^8*r^4+54*cos(theta)^4*a^10*r^2+189*cos(theta)^4*a^8*r^4+222*cos(theta)^4*a^6*r^6-81*cos(theta)^2*a^8*r^4-162*cos(theta)^2*a^6*r^6-69*cos(theta)^2*a^4*r^8-3*r^12-18*cos(theta)^8*a^8*r^4-90*cos(theta)^6*a^6*r^6+87*cos(theta)^4*a^4*r^8+12*cos(theta)^2*a^2*r^10)*m^2/((a^2-2*m*r+r^2)*(r^2+a^2*cos(theta)^2)^8)

 (2)
> 

simplify(factor(expand(combine(expr3), trig)))

-48*m^2*(a^6*(a^2-2*m*r+r^2)*cos(theta)^6+(-15*a^6*r^2+30*a^4*m*r^3)*cos(theta)^4+15*a^2*r^4*(a^2*sin(theta)^2-2*m*r+r^2)*cos(theta)^2-a^2*r^6+2*m*r^7-r^8)/((r^2+a^2*cos(theta)^2)^6*(a^2-2*m*r+r^2))

 (3)


 

Download QuestionSimplifyMultivariateRationalFunction_DOS.mw

SOLVED, thanks...

ignacios 10
March 10 2024
0 0


I rephrase my question and add the solutions:

I have the following expressions:

expr1 := m^3*r*(cos(theta)^6*a^6-9*cos(theta)^4*a^4*r^2+11*cos(theta)^2*a^2*r^4-(1/3)*r^6)*(cos(theta)^2*a^2-(1/3)*r^2)/(r^2+cos(theta)^2*a^2)^9

expr2 := (a^8*(r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8-80*m^3*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(1/3)*(28*(-30*sin(theta)^2*a^4*m*r^5*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(32*(-5*a^2*m^3-m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^6*r^2*cos(theta)^6+(14*(-260*sin(theta)^2*a^6*m*r^3*(1/7)+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4-80*a^4*m^3*r^3+(5*(a^8+8*a^6*m^2))*r^2-10*a^8*m*r+a^10))*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+(5*(a^2+8*m^2))*r^8+(40*(-a^2*m-2*m^3))*r^7+(10*(a^4+12*a^2*m^2+8*m^4))*r^6+(4*(-15*a^4*m-40*a^2*m^3-8*m^5))*r^5+(10*(a^6+12*a^4*m^2+8*a^2*m^4))*r^4+(40*(-a^6*m-2*a^4*m^3))*r^3+(5*(a^8+8*a^6*m^2))*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+a^2*cos(theta)^2)^9*(a^2-2*m*r+r^2)^5)

The two expressions are the same because:

simplify(expr1-expr2)

0

 (1)

But I don't get the expression (1) from (2) with the help of simplify() command:

simplify(expr2)

(a^8*(r^10-10*m*r^9+5*(a^2+8*m^2)*r^8-80*m^3*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*cos(theta)^8-(28/3)*(-(30/7)*sin(theta)^2*a^4*m*r^5+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+32*(-5*a^2*m^3-m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^6*r^2*cos(theta)^6+14*(-(260/7)*sin(theta)^2*a^6*m*r^3+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4-80*a^4*m^3*r^3+5*(a^8+8*a^6*m^2)*r^2-10*a^8*m*r+a^10)*a^4*r^4*cos(theta)^4-4*a^2*(-10*a^8*m*r*sin(theta)^2+r^10-10*m*r^9+5*(a^2+8*m^2)*r^8+40*(-a^2*m-2*m^3)*r^7+10*(a^4+12*a^2*m^2+8*m^4)*r^6+4*(-15*a^4*m-40*a^2*m^3-8*m^5)*r^5+10*(a^6+12*a^4*m^2+8*a^2*m^4)*r^4+40*(-a^6*m-2*a^4*m^3)*r^3+5*(a^8+8*a^6*m^2)*r^2+a^10)*r^6*cos(theta)^2+(1/9)*r^8*(a^2-2*m*r+r^2)^5)*m^3*r/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (2)

Why not? Is there any solution for this?

SOLUTIONS:

factor(expand(combine(expr2), trig))``

(1/9)*r*m^3*(3*cos(theta)^2*a^2-r^2)*(3*cos(theta)^6*a^6-27*cos(theta)^4*a^4*r^2+33*cos(theta)^2*a^2*r^4-r^6)/(r^2+cos(theta)^2*a^2)^9

 (3)

``normal(expand(combine(expr2), trig))NULL

(1/9)*r*m^3*(9*a^8*cos(theta)^8-84*a^6*r^2*cos(theta)^6+126*a^4*r^4*cos(theta)^4-36*a^2*r^6*cos(theta)^2+r^8)/(r^2+cos(theta)^2*a^2)^9

 (4)

With Maple 2024.0, the following does not do the desired work:``

factor(simplify(expr2))

(1/9)*m^3*r*(5040*a^10*r^6*cos(theta)^4*m^2-10080*a^8*r^7*cos(theta)^4*m^3+15120*a^8*r^8*cos(theta)^4*m^2-7560*a^8*r^9*cos(theta)^4*m+10080*a^6*r^8*cos(theta)^4*m^4-20160*a^6*r^9*cos(theta)^4*m^3+15120*a^6*r^10*cos(theta)^4*m^2-5040*a^6*r^11*cos(theta)^4*m-4032*a^4*r^9*cos(theta)^4*m^5+10080*a^4*r^10*cos(theta)^4*m^4-10080*a^4*r^11*cos(theta)^4*m^3+5040*a^4*r^12*cos(theta)^4*m^2-1260*a^4*r^13*cos(theta)^4*m-1440*cos(theta)^2*a^8*m^2*r^8+1440*cos(theta)^2*a^8*m*r^9+2880*cos(theta)^2*a^6*m^3*r^9-4320*cos(theta)^2*a^6*m^2*r^10+2160*cos(theta)^2*a^6*m*r^11-2880*cos(theta)^2*a^4*m^4*r^10+5760*cos(theta)^2*a^4*m^3*r^11-4320*cos(theta)^2*a^4*m^2*r^12+1440*cos(theta)^2*a^4*m*r^13+1152*cos(theta)^2*a^2*m^5*r^11-2880*cos(theta)^2*a^2*m^4*r^12+2880*cos(theta)^2*a^2*m^3*r^13-1440*cos(theta)^2*a^2*m^2*r^14+360*cos(theta)^2*a^2*m*r^15-90*cos(theta)^8*a^16*m*r+360*cos(theta)^8*a^14*m^2*r^2-360*cos(theta)^8*a^14*m*r^3-720*cos(theta)^8*a^12*m^3*r^3+1080*cos(theta)^8*a^12*m^2*r^4-540*cos(theta)^8*a^12*m*r^5+720*cos(theta)^8*a^10*m^4*r^4-1440*cos(theta)^8*a^10*m^3*r^5+1080*cos(theta)^8*a^10*m^2*r^6-288*cos(theta)^8*a^8*m^5*r^5+720*cos(theta)^8*a^8*m^4*r^6-720*cos(theta)^8*a^8*m^3*r^7+360*cos(theta)^8*a^8*m^2*r^8-90*cos(theta)^8*a^8*m*r^9+840*a^14*r^3*cos(theta)^6*m-3360*a^12*r^4*cos(theta)^6*m^2+3360*a^12*r^5*cos(theta)^6*m+6720*a^10*r^5*cos(theta)^6*m^3-10080*a^10*r^6*cos(theta)^6*m^2-6720*a^8*r^6*cos(theta)^6*m^4+13440*a^8*r^7*cos(theta)^6*m^3-10080*a^8*r^8*cos(theta)^6*m^2+3360*a^8*r^9*cos(theta)^6*m+2688*a^6*r^7*cos(theta)^6*m^5-6720*a^6*r^8*cos(theta)^6*m^4+6720*a^6*r^9*cos(theta)^6*m^3-3360*a^6*r^10*cos(theta)^6*m^2+840*a^6*r^11*cos(theta)^6*m-1260*a^12*r^5*cos(theta)^4*m+45*cos(theta)^8*a^16*r^2+90*cos(theta)^8*a^14*r^4+90*cos(theta)^8*a^12*r^6+45*cos(theta)^8*a^10*r^8+9*cos(theta)^8*a^8*r^10-84*a^16*r^2*cos(theta)^6-420*a^14*r^4*cos(theta)^6-840*a^12*r^6*cos(theta)^6-840*a^10*r^8*cos(theta)^6-420*a^8*r^10*cos(theta)^6-84*a^6*r^12*cos(theta)^6+126*a^14*r^4*cos(theta)^4+630*a^12*r^6*cos(theta)^4+1260*a^10*r^8*cos(theta)^4+1260*a^8*r^10*cos(theta)^4+630*a^6*r^12*cos(theta)^4+126*a^4*r^14*cos(theta)^4-36*cos(theta)^2*a^12*r^6-180*cos(theta)^2*a^10*r^8-360*cos(theta)^2*a^8*r^10-360*cos(theta)^2*a^6*r^12-180*cos(theta)^2*a^4*r^14-36*cos(theta)^2*a^2*r^16+r^18+9*cos(theta)^8*a^18-10*a^8*m*r^9+40*a^6*m^2*r^10-40*a^6*m*r^11-80*a^4*m^3*r^11+120*a^4*m^2*r^12-60*a^4*m*r^13+80*a^2*m^4*r^12-160*a^2*m^3*r^13+120*a^2*m^2*r^14-40*a^2*m*r^15+a^10*r^8+5*a^8*r^10+10*a^6*r^12+10*a^4*r^14+5*a^2*r^16-32*m^5*r^13+80*m^4*r^14-80*m^3*r^15+40*m^2*r^16-10*m*r^17+360*a^10*r^7*cos(theta)^6*sin(theta)^2*m-4680*a^10*r^7*cos(theta)^4*sin(theta)^2*m+360*cos(theta)^2*sin(theta)^2*a^10*m*r^7)/((r^2+cos(theta)^2*a^2)^9*(a^2-2*m*r+r^2)^5)

 (5)

Alternatively you can write like this:

(`@`(`@`(factor, expand), combine))(expr2, trig)

(1/9)*r*m^3*(3*cos(theta)^2*a^2-r^2)*(3*cos(theta)^6*a^6-27*cos(theta)^4*a^4*r^2+33*cos(theta)^2*a^2*r^4-r^6)/(r^2+cos(theta)^2*a^2)^9

 (6)

(`@`(`@`(normal, expand), combine))(expr2, trig)

(1/9)*r*m^3*(9*a^8*cos(theta)^8-84*a^6*r^2*cos(theta)^6+126*a^4*r^4*cos(theta)^4-36*a^2*r^6*cos(theta)^2+r^8)/(r^2+cos(theta)^2*a^2)^9

 (7)

NULL


 

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