Question

Reduce to lowest terms...

Answer 1

x^3+8y^3 over x^2+2xy

Answer 2

@ganeshie8

Answer 3

There isn't really anything else you can do to it

Answer 4

please help i cant leave it like that @larryboxaplenty

Answer 5

Simplify the following:
(x^3+8 y^3)/(x^2+2 x y)

Factor common terms out of x^2+2 x y.

Factor x out of x^2+2 x y:
(x^3+8 y^3)/x (x+2 y)

Write 8 y^3 as a cube in order to express x^3+8 y^3 as a sum of cubes.
x^3+8 y^3 = x^3+(2 y)^3:
(x^3+(2 y)^3)/(x (x+2 y))

Factor the sum of two cubes. x^3+(2 y)^3 = (x+2 y) (x^2-x×2 y+(2 y)^2):
(x+2 y) (x^2-2 x y+(2 y)^2)/(x (x+2 y))

Distribute exponents over products in (2 y)^2.

Multiply each exponent in 2 y by 2:
((x+2 y) (x^2-2 x y+2^2 y^2))/(x (x+2 y))

Evaluate 2^2.
2^2 = 4:
((x+2 y) (x^2-2 x y+4 y^2))/(x (x+2 y))

Cancel common terms in the numerator and denominator of ((x+2 y) (x^2-x×2 y+4 y^2))/(x (x+2 y)).
((x+2 y) (x^2-x×2 y+4 y^2))/(x (x+2 y)) = (x+2 y)/(x+2 y)×(x^2-2 x y+4 y^2)/x = (x^2-2 x y+4 y^2)/x:
Answer: (x^2-2 x y+4 y^2)/x

Which can be further reduced to (4 y^2)/x+x-2 y