(n+2)(n^2+5n-3)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (n+2)(n^2+5n-3)

This article will guide you through the process of expanding the given expression: (n+2)(n^2+5n-3). 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

1. 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

2. 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

3. Combine the results:

   • Now we have: n^3 + 5n^2 - 3n + 2n^2 + 10n - 6

4. Simplify by combining like terms:

   • n^3 + (5n^2 + 2n^2) + (-3n + 10n) - 6

5. Final expanded form:

   • n^3 + 7n^2 + 7n - 6

Conclusion

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