Final answer:
The algebraic expression for the product of a number and 4 more than the number is n(n + 4), which expands to n² + 4n.
Step-by-step explanation:
The algebraic expression for the product of a number and 4 more than the number would be represented by n(n + 4). Here, 'n' represents the number in question. If we break this down, the first 'n' essentially shows the number itself, and '(n + 4)' indicates 4 more than the number. When these two are multiplied, it gives the product of the number and 4 more than the number.
This expression fits the standard form of algebraic multiplication, where we apply the concept that raising a number to a given power is equivalent to multiplying the number by itself a certain number of times, although in this case, we are not dealing with exponents or powers.
When we solve this expression, we first apply the distributive property: n multiplied by n is n² (n squared), and n multiplied by 4 is 4n. Therefore, the expanded form of the algebraic expression would be n² + 4n.