How do I do this algebra problem? Factor the sum of two cubes: x^3 y^3+64?

Question

Factor the sum of two cubes: x to the third and y to the third plus 64.

Answer 1

this factors to

(x³ y³ + 64) =(xy+4) (x² y² - 4xy + 16)

Answer 2

One can factorize x³y³ + 64, using the formula:

a³ + b³ = (a + b)(a² - ab + b²).....(1)

Now write: x³ y³ + 64 = (xy)³ + 4³

= (xy + 4)(x²y² - xy + 16), using (1), a = xy, b = 4.

Answer 3

x^3y^3+64=0
taking cube common for x*y
(x*y)^3+(4)^3 =0 (since cube th root of 64 is 4 iam writing like this)

taking cube th root
x*y+4=0
x=-4/y

Answer 4

bear in mind that the formula for the sum of two cubes is: a³ + b³ = (a + b)(a² - ab + b²) enable: a³ = sixty 4 a = sixty 4^(a million/3) a = 4 b³ = a³ b = a So the climate are: (4 + a)(4² - 4a + a²) ==> (4 + a)(sixteen - 4a + a²) i wish this helps!