Evaluate :
( a )` ( y^2 + 2/3 ) ( y^2 - 2/3 )`
( b ) `( 3 - x^2 ) ( 3 + x^2 )`

Factorize : ( 2x + 3y )^2 + 2 (2x + 3y ) ( x + y ) + ( x + y )^2

3 - [x - {2y - (5x + y - 3) + 2x^(2)} - (x^(2) - 3y)]

if (x_ (1), y_ (1)), (x_ (2), y_ (2)), (x_ (3), y_ (3)) are vertices equilateral triangle such that (x_ (1) -2) ^ (2) + (y_ (1) -3) ^ (2) = (x_ (2) -2) ^ (2) + (y_ (2) -3) ^ (2) = (x_ (3) - 2) ^ (2) + (y_ (3) -3) ^ (2) then x_ (1) + x_ (2) + x_ (3) +2 (y_ (1) + y_ (2) + y_ (3) ))

The value of the expression ((x ^(2) - y ^(2)) ^(3) + ( y ^(2) - z ^(2)) ^(3) + (z ^(2) - x ^(2)) ^(3))/((x - y) ^(3) + ( y - z) ^(3) + (z - x ) ^(3)) is

Evaluate: (2x+3y)^(2)( ii) (2x-3y)^(2)(2x+3y)2x-3y)

Evaluate : 1/2 x^2y^2 times ( -1/4x^3y^3 ) times ( x^3y^3) times x^2y^2

Evaluate : 1/2 x^2y^2 times ( -1/4x^3y^3 ) times ( x^3y^3) times x^2y^2

The following steps are involved in expanding (x+ 3y)^(2) . Arrange them in sequential order from the first to the last . (A) (x + 3y)^(2) = x^(2) + 6xy + 9y^(2) (B) (x + 3y)^(2) = (x)^(2) + 2(x)(3y) + (3y)^(2) (C) Using the identify (a + b)^(2) = a^(2) + 2ab + b^(2) , where a = x and b = 3y.