If x+y=5, then what is the value of x3+y3+15xy

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