`(a^2 b - b^2 a )^2`

Verify that (a ^(2) - b ^(2)) (a ^(2) + b ^(2)) + (b ^(2) - c ^(2)) (b ^(2) + c ^(2)) + (c ^(2)-a ^(2)) + (c ^(2) + a ^(2)) = 0

Find the value of ( a^2/b^2 + b^2/a^2 ) is ( a ) ( a/b + b/a )^2 - 2 ( b ) ( a/b + b/a )^2 + 2 ( c ) ( a/b + b/a )^2 + 4 ( d ) ( a/b + b/a )^2 - 4

Factorise : (a^2 - b^2) c + (b^2 - c^2) a

{:("Column A",a = 49"," b = 59,"Column B"),((a^2 - b^2)/(a - b),,(a^2 - b^2)/(a + b)):}

If a, b, c are in G.P. , then show that (i) (a^(2) - b^(2))(b^(2) + c^(2)) = (b^(2) -c^(2)) (a^(2) + b^(2)) (ii) a( b^(2) + c^(2)) = c (a^(2) + b^(2))

Simplify each of the following algebraic expressions: (a^2+b^2+2a b)+(a^2+b^2-2a b) (a^2+b^2+2a b)-(a^2+b^2-2a b)

Simplify each of the following algebraic expressions: (i) (a^2+b^2+2a b)+(a^2+b^2-2a b) (ii) (a^2+b^2+2a b)-(a^2+b^2-2a b)

If : cot theta =(a)/(b), "then" : a *cos 2 theta +b * sin 2 theta= A) a^(2) +b^(2) B) a^(2) - b^(2) C)a D)b