(2x+3)(3x2+x+5) In Standard Form

Jasonbradley

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Jun 16, 2024

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Expanding and Simplifying (2x+3)(3x^2+x+5)

This article will guide you through the process of expanding and simplifying the expression (2x+3)(3x^2+x+5) to obtain its standard form.

Understanding the Process

The expression (2x+3)(3x^2+x+5) represents the product of two binomials. To expand this, we'll employ the distributive property (also known as FOIL - First, Outer, Inner, Last).

Expanding the Expression

1. Multiply the first terms of each binomial: (2x) * (3x^2) = 6x^3

2. Multiply the outer terms of the binomials: (2x) * (x) = 2x^2

3. Multiply the inner terms of the binomials: (3) * (3x^2) = 9x^2

4. Multiply the last terms of each binomial: (3) * (x) = 3x

5. Multiply the last terms of each binomial: (3) * (5) = 15

6. Combine all the terms: 6x^3 + 2x^2 + 9x^2 + 3x + 15

Simplifying the Expression

Now, we combine like terms to simplify the expanded expression:

6x^3 + 11x^2 + 3x + 15

Conclusion

Therefore, the standard form of the expression (2x+3)(3x^2+x+5) is 6x^3 + 11x^2 + 3x + 15.