" (i) "x^(3)-y^(3)=(x-y)(x^(2)+xy+y^(2))

Verify x^(3)+y^(3)=(x+y)(x^(2)-xy+y^(2)) using some non-zero positive integers and check by actual multiplication. Can you call these as identites ?

Verify x^(3)-y^(3)= (x-y)(x^(2)+y^(2)+xy) Hence factorise 216x^(3)-125y^(3)

The factors of x^(3)-x^(2)y-xy^(2)+y^(3) are (a (x+y)(x^(2)-xy+y^(2))(b)(x+y)(x^(2)+xy+y^(2))(c)(x+y)^(2)(x-y)(d)(x-y)^(2)(x+y)

Simplify: (x^(3)-y^(3))/(3x^(2)+9xy+6y^(2))xx(x^(2)+2xy+y^(2))/(x^(2)-y^(2))

Verify : x^3-y^3=(x-y)(x^2+xy+y^2) .

The following are the steps involved in factorizing 64 x^(6) -y^(6) . Arrange them in sequential order (A) {(2x)^(3) + y^(3)} {(2x)^(3) - y^(3)} (B) (8x^(3))^(2) - (y^(3))^(2) (C) (8x^(3) + y^(3)) (8x^(3) -y^(3)) (D) (2x + y) (4x^(2) -2xy + y^(2)) (2x - y) (4x^(2) + 2xy + y^(2))

If x:y::5:2, then (x ^(3) - y ^(3))/( x ^(3) + y ^(3)) = ?