x^(a)*y^(b)=(x-y)^(a+b)

Factorize each of the following algebraic expressions: x^(3)(a-2b)+x^(2)(a-2b)2x-3y)(a+b)+(3x-2y)(a+b)4(x+y)(3a-b)+6(x+y)(2b-3a)

Prove that the diagonals of the parallelogram formed by the four lines : (x)/(a)+(y)/(b)=1 , (x)/(a)+(y)/(b)=-1 , (x)/(a)-(y)/(b)=1 , (x)/(a)-(y)/(b)=-1 are at right angles.

The expression ((x+(1)/(y))^(a)*(x-(1)/(y))^(b))/((y+(1)/(x))^(a)*(y-(1)/(x))^(b)) reduces to a.((x)/(y))^(a-b) b.((y)/(x))^(a-b)backslash c((x)/(y))^(a+b)d.((y)/(x))^(a+b)

Prove that the parallelogram formed by the straight lines : (x)/(a)+(y)/(b)=1 , (x)/(b)+(y)/(a)=1 , (x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 is a rhombus.

Straight lines (x)/(a)+(y)/(b)=1, (x)/(b)+(y)/(a)=1,(x)/(a)+(y)/(b)=2 and (x)/(b)+(y)/(a)=2 form a rhombus of area ( in square units)

Prove that the following sets of three lines are concurrent: (x)/(a)=(y)/(b)=1,(x)/(b)+(y)/(a)=1 and y=x

Solve the following system of equations : (2x)/(a)+(y)/(b)=2, (x)/(a)-(y)/(b)=4:

Factorize each of the following algebraic expressions: (i) x^3(a-2b)+x^2(a-2b) (ii)2x-3y)(a+b)+(3x-2y)(a+b) (iii)4\ (x+y)(3a-b)+6(x+y)(2b-3a)