Use Pascal's Triangle to expand left bracket, 3, x, squared, plus, 3, y, right bracket, cubed(3x
2
+3y)
3
. Express your answer in simplest form.
Expanding the given expression using Pascal's Triangle, we have:
(3x^2 + 3y)^3
Using the third row of Pascal's Triangle, the expansion is:
(1)^3(3x^2)^3 + (3)(1)^2(3x^2)^2(3y) + (3)(1)(3x^2)(3y)^2 + (1)^3(3y)^3
Simplifying each term, we get:
(1)(27x^6) + (3)(9x^4)(3y) + (9x^2)(9y^2) + (1)(27y^3)
Simplifying further, we have:
27x^6 + 81x^4y + 81x^2y^2 + 27y^3
Therefore, the expanded form of (3x^2 + 3y)^3 is 27x^6 + 81x^4y + 81x^2y^2 + 27y^3.