Expanding the Expression: (n+2)(n^2+5n3)
This article will guide you through the process of expanding the given expression: (n+2)(n^2+5n3). This is a basic algebraic operation involving multiplication of two polynomials.
The Distributive Property
To expand this expression, we'll utilize the distributive property of multiplication. This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
Expanding the Expression

Distribute the first term (n):
 Multiply 'n' by each term inside the second set of parentheses:
 n * n^2 = n^3
 n * 5n = 5n^2
 n * 3 = 3n
 Multiply 'n' by each term inside the second set of parentheses:

Distribute the second term (2):
 Multiply '2' by each term inside the second set of parentheses:
 2 * n^2 = 2n^2
 2 * 5n = 10n
 2 * 3 = 6
 Multiply '2' by each term inside the second set of parentheses:

Combine the results:
 Now we have: n^3 + 5n^2  3n + 2n^2 + 10n  6

Simplify by combining like terms:
 n^3 + (5n^2 + 2n^2) + (3n + 10n)  6

Final expanded form:
 n^3 + 7n^2 + 7n  6
Conclusion
Therefore, the expanded form of the expression (n+2)(n^2+5n3) is n^3 + 7n^2 + 7n  6. This process demonstrates how the distributive property can be applied to expand expressions involving polynomials.