(x+4)(x2+7x)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (x+4)(x^2 + 7x)

This article will guide you through the process of expanding the expression (x+4)(x^2 + 7x). This is an example of multiplying two binomials, one of which is a trinomial. We can achieve this using the distributive property.

The Distributive Property

The distributive property states that a(b + c) = ab + ac. This means we can distribute the factor outside the parentheses to each term inside the parentheses.

Expanding the Expression

1. Distribute the first term:

   • Multiply x by each term in the second parentheses:
     • x * x^2 = x^3
     • x * 7x = 7x^2

2. Distribute the second term:

   • Multiply 4 by each term in the second parentheses:
     • 4 * x^2 = 4x^2
     • 4 * 7x = 28x

3. Combine the terms:

   • We now have: x^3 + 7x^2 + 4x^2 + 28x
   • Combine like terms: x^3 + 11x^2 + 28x

Final Answer

Therefore, the expanded form of (x+4)(x^2 + 7x) is x^3 + 11x^2 + 28x.