`ab(x^(2)+y^(2))-xy(a^(2)+b^(2))`

Factorise the following expressions : (i) ax-ay+bx-by " " (ii) x^(2)-x-ax+a " " (iii) x^(4)+x^(3)+x^(2)+x (iv) 16(a+b)^(2)-4a-4b " " (v) x^(2)+(1)/(x^(2))+2-3x-(3)/(x) " " (vi) x^(2)-((a)/(b)+(b)/(a))x+1 (vii) x^(2)+(a-(1)/(a))x-1 " " (viii)ab(x^(2)+y^(2)+xy(a^(2)+b^(2)) " "(ix) (ax+by)^(2)+(bx-ay)^(2)

If (x+1)/(x-1)=(a)/(b) and (1-y)/(1+y)=(b)/(a), then the value of (x-y)/(1+xy) is (2ab)/(a^(2)-b^(2)) (b) (a^(2)-b^(2))/(2ab) (c) (a^(2)+b^(2))/(2ab) (d) (a^(2)-b^(2)backslash)/(ab)

If a=(x)/(x+y) and b=(y)/(x-y), then (ab)/(a+b) is equal to (a) (xy)/(x^(2)+y^(2)) (b) (x^(2)+y^(2))/(xy)( c) (x)/(x+y) (d) ((y)/(x+y))^(2)

If cos^(-1)(x/a)+cos^(-1)(y/b)=theta ,then the value of sqrt((x^(2))/(a^(2))+(y^(2))/(b^(2))-(2xy)/(ab)cos theta) is equal to

Factorize each of the following expressions: x^(2)+2xy+y^(2)-a^(2)+2ab-b^(2)

Factorize each of the following expressions: x^(2)+2xy+y^(2)-a^(2)+2ab-b^(2)25x^(2)-10x+1-36y^(2)1-2ab-(a^(2)+b^(2))

Solve for x and y. (a-b)x+(a+b)y=a^(2)-2ab-b^(2) , (a+b)(x+y)=a^(2)+b^(2)

Solve :a(x+y)+b(x-y)=a^(2)-ab+b^(2)a(x+y)-b(x-y)=a^(2)+ab+b^(2)

If cos^(-1) . x/a - sin^(-1). y/b = theta (a , b , ne 0) , then the maximum value of b^(2) x^(2) + a^(2) y^(2) + 2ab xy sin theta equals