x3-y3
When it is of the form x3 + y3 or x3 - y3. x or y can have coefficients that are perfect cubes, or even ratios of perfect cubes eg x3 + (8/27)y3.
x^2 - xy + y^2
It is an algebraic expression.
(x4 + y4)/(x + y) = Quotient = x3 - x2y + xy2 - y3 Remainder = - 2y4/(x+y) So, x3 - x2y + xy2 - y3 - 2y4/(x+y)
x6 - y6 = (x3)2 - (y3)2 = (x3 + y3) (x3 - y3) = (x + y)(x2 - xy + y2)(x - y)(x2 + xy + y2)
x3-y3
(x2 - xy + y2)(x + y)
(x - y)(x^2 + xy + y^2
x^2 - xy + y^2
When it is of the form x3 + y3 or x3 - y3. x or y can have coefficients that are perfect cubes, or even ratios of perfect cubes eg x3 + (8/27)y3.
It is an algebraic expression.
3xyz
The required result will be 3xyz
That's either the sum or difference of two cubes.
When one thing is a multiple of the other, it's automatically the LCM. 16 is a multiple of 8. x3 is a multiple of x2 y3 is a multiple of y2 and z is a multiple of z. That makes the answer 16x3y3z
(x4 + y4)/(x + y) = Quotient = x3 - x2y + xy2 - y3 Remainder = - 2y4/(x+y) So, x3 - x2y + xy2 - y3 - 2y4/(x+y)