Final answer:
To determine the number of nonzero terms in the expansion of the given expression, we need to distribute and simplify. After expanding and combining like terms, we find that the expression has 4 nonzero terms.
Step-by-step explanation:
To determine the number of nonzero terms in the expansion of the given expression, we need to distribute and simplify. Let's start with the first term:
(x + 4)(2x^2 + 3x + 9)
Expanding:
2x^3 + 3x^2 + 9x + 8x^2 + 12x + 36
Combining like terms:
2x^3 + 11x^2 + 21x + 36
Now let's focus on the second term:
-3(x^3 - 2x^2 + 7x)
Distributing:
-3x^3 + 6x^2 - 21x
Combining like terms:
-3x^3 + 6x^2 - 21x
Adding the two simplified terms together:
2x^3 + 11x^2 + 21x + 36 + (-3x^3 + 6x^2 - 21x)
Combining like terms:
-x^3 + 17x^2 + 15x + 36
Therefore, the number of nonzero terms in the expansion is 4.