Please help! (X+y)^3+(x-y)^3

a^3-b^3 = (a-b)(a^2+ab+b^2)

So, using a=x+y and b=x-y

(x+y)^3 - (x-y)^3
= ((x+y)-(x-y))((x+y)^2+(x+y)(x-y)+(x-y)^2)
= (2y)(x^2+2xy+y^2+x^2-y^2+x^2-2xy+y^2)
= (2y)(3x^2+y^2)

Thanks so much steve!

Certainly! To simplify the expression (x+y)^3 + (x-y)^3, we can use a combination of the binomial expansion formula and simplifying techniques.

The binomial expansion formula states that (a+b)^n = nCr * a^(n-r) * b^r, where nCr represents the number of combinations of choosing r items from n.

In this case, we have (x+y)^3 + (x-y)^3.
Expanding the first term, we have:
(x+y)^3 = 1C0 * x^3 * y^0 + 3C1 * x^2 * y^1 + 3C2 * x^1 * y^2 + 1C3 * x^0 * y^3
= x^3 + 3x^2y + 3xy^2 + y^3

Expanding the second term, we have:
(x-y)^3 = 1C0 * x^3 * (-y)^0 + 3C1 * x^2 * (-y)^1 + 3C2 * x^1 * (-y)^2 + 1C3 * x^0 * (-y)^3
= x^3 - 3x^2y + 3xy^2 - y^3

Now, we can add the two expanded terms together:
(x+y)^3 + (x-y)^3 = (x^3 + 3x^2y + 3xy^2 + y^3) + (x^3 - 3x^2y + 3xy^2 - y^3)
= 2x^3 + 6xy^2

Therefore, (x+y)^3 + (x-y)^3 simplifies to 2x^3 + 6xy^2.