Answer:
125
Step-by-step explanation:
x + y = 5
We need to have x^3 and y^3 in the expression, so cube both sides.
(x + y)^3 = 5^3
Expand the left side.
(x + y)(x + y)^2 = 125
(x + y)(x^2 + 2xy + y^2) = 125
x^3 + 2x^2y + xy^2 + x^2y + 2xy^2 + y^3 = 125
x^3 + 3x^2y + 3xy^2 + y^3 = 125
Now we need to separate x^3 + y^3.
x^3 + y^3 + 3x^2y + 3xy^2 = 125
We need to turn 3x^2y + 3xy^2 into 15xy.
Factor the GCF, 3xy, out of 3x^2y + 3xy^2.
x^3 + y^3 + 3xy(x + y) = 125
We know that x + y = 5, so substitute x + y with 5.
x^3 + y^3 + 3xy(5) = 125
x^3 + y^3 + 15xy = 125
Answer: 125
