(x+2)(x^2+5x+1)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (x+2)(x^2+5x+1)

This article will guide you through expanding the expression (x+2)(x^2+5x+1). We will use the distributive property to achieve this.

Understanding the Distributive Property

The distributive property states that: a(b+c) = ab + ac

This means we can multiply each term inside the parentheses by the term outside the parentheses.

Applying the Distributive Property

1. Distribute the 'x' term:

   • x(x^2 + 5x + 1) = x^3 + 5x^2 + x

2. Distribute the '2' term:

   • 2(x^2 + 5x + 1) = 2x^2 + 10x + 2

3. Combine the results:

   • x^3 + 5x^2 + x + 2x^2 + 10x + 2

4. Simplify by combining like terms:

   • x^3 + 7x^2 + 11x + 2

Conclusion

Therefore, the expanded form of (x+2)(x^2+5x+1) is x^3 + 7x^2 + 11x + 2. This process can be applied to any similar expression involving multiplication of polynomials.