(2x+1)(x+4) Answer

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x + 1)(x + 4)

This article will demonstrate how to expand the expression (2x + 1)(x + 4).

Understanding the Process

Expanding this expression involves using the distributive property of multiplication. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number.

Step-by-Step Solution

1. Distribute the first term (2x) from the first binomial:

   (2x)(x + 4) = 2x² + 8x

2. Distribute the second term (1) from the first binomial:

   (1)(x + 4) = x + 4

3. Combine the results from steps 1 and 2:

   2x² + 8x + x + 4

4. Simplify by combining like terms:

   2x² + 9x + 4

Conclusion

Therefore, the expanded form of (2x + 1)(x + 4) is 2x² + 9x + 4. This process of expanding binomials is fundamental in algebra and is used extensively in solving equations, simplifying expressions, and understanding various algebraic concepts.