If `a+b=1` then prove that `a^3+b^3+3ab=1`

if a=3+b then prove that a^3-b^3-9ab=27

If a : b = b : c , then prove that (abc(a+b+c)^(3))/((ab+bc+ca)^(3)) = 1

If a+b+c=0 , then prove that (b+c)^2/(3bc )+ (c+a)^2/(3ca )+ (a+b)^2/(3ab )=1

if a=3+b, prove that a^(3)-b^(3)-9ab=27

If x = a^(1/3) b^(-1/3) + a^(-1/3) b^(1/3) then prove that a(bx^(3) - 3bx -a) = b^(2)

If a+b+c=0, then prove that ((b+c)^(2))/(3bc)+((c+a)^(2))/(3ac)+((a+b)^(2))/(3ab)=1

If a-b=1, then the value of a^(3)-b^(3)-3ab will be -3(b)-1(c)1(d)3

If x = a^((1)/(3)) b^((1)/(3)) + a^(-(1)/(3)) + a^(-(1)/(3)) b^((1)/(3)) then prove that a(bx^(3) - 3bx - a) = b^(2)

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .

If A and B are square matrices such that AB = BA then prove that A^(3)-B^(3)=(A-B) (A^(2)+AB+B^(2)) .