Final answer:
To expand the expression (5z+2y^(2))^(3) using Pascal's Triangle, we can use the binomial theorem. The binomial theorem states that for any positive integer n, the expansion of (a+b)^n can be written as...
Step-by-step explanation:
To expand the expression (5z+2y^(2))^(3) using Pascal's Triangle, we can use the binomial theorem. The binomial theorem states that for any positive integer n, the expansion of (a+b)^n can be written as: (a+b)^n = C(n,0)a^n + C(n,1)a^(n-1)b + C(n,2)a^(n-2)b^2 + ... + C(n,n)b^n, where C(n,r) denotes the binomial coefficient.
In this case, a = 5z and b = 2y^(2), and we are expanding to the power of 3. So the expanded form is:
(5z+2y^(2))^(3) = C(3,0)(5z)^3 + C(3,1)(5z)^(3-1)(2y^(2))^1 + C(3,2)(5z)^(3-2)(2y^(2))^2 + C(3,3)(2y^(2))^3