Let f(x) = 27x^5 + 33x^4 + 21x^3 and g(x) = 3x^2. Find f(x)g(x).

To find the product of the functions f(x) and g(x), we need to multiply the two expressions together:

f(x) = 27x⁵ + 33x⁴ + 21x³

g(x) = 3x²

The product f(x)g(x) can be calculated as follows:

f(x)g(x) = (27x⁵ + 33x⁴ + 21x³)(3x²)

Now we distribute 3x² to each term in f(x):

• 3x² * 27x⁵ = 81x⁷
• 3x² * 33x⁴ = 99x⁶
• 3x² * 21x³ = 63x⁵

Putting it all together, we have:

f(x)g(x) = 81x⁷ + 99x⁶ + 63x⁵

This is the product of the two functions.