Maximizing Product of Two Parts:
To maximize the product of two parts, we need to split 30 into two parts such that their product is as large as possible. Let's denote the two parts as x and 30-x.

Setting up the Equation:
The product of the two parts is given by x * (30-x). To maximize this product, we need to find the value of x that will yield the highest result.

Calculating the Product:
Expanding the product gives us 30x - x^2. To find the maximum product, we need to differentiate this expression with respect to x and set it equal to zero.

Finding the Maximum Product:
Differentiating 30x - x^2 with respect to x gives us 30 - 2x. Setting this equal to zero and solving for x, we get x = 15. Therefore, the two parts are 15 and 15, giving us a maximum product of 225.

Conclusion:
To maximize the product of two numbers that sum up to a constant, split the number into two equal parts. In this case, splitting 30 into 15 and 15 gives us the maximum product of 225.