## Simplifying the Expression (x+3)(2x^2-3x+4)

This article will guide you through the process of simplifying the expression (x+3)(2x^2-3x+4). This involves applying the distributive property of multiplication.

### Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by the number and then adding the products. In simpler terms:

**a(b + c) = ab + ac**

### Applying the Distributive Property

**Treat (x+3) as a single term.**We need to distribute each term inside (x+3) to all terms inside (2x^2-3x+4).**Multiply x by each term inside the second parenthesis.**- x * 2x^2 = 2x^3
- x * -3x = -3x^2
- x * 4 = 4x

**Multiply 3 by each term inside the second parenthesis.**- 3 * 2x^2 = 6x^2
- 3 * -3x = -9x
- 3 * 4 = 12

**Combine all the terms.**- 2x^3 - 3x^2 + 4x + 6x^2 - 9x + 12

### Simplifying the Expression

Combine the like terms:

**2x^3**- 3x^2 + 6x^2 + 4x - 9x + 12

This simplifies to:

**2x^3 + 3x^2 - 5x + 12**

### Conclusion

Therefore, the simplified form of the expression (x+3)(2x^2-3x+4) is **2x^3 + 3x^2 - 5x + 12**. Understanding the distributive property and applying it systematically is key to simplifying expressions like this.