(2x%5E2-3x%2B4)-simplify.jpeg "(x+3)(2x^2-3x+4) Simplify")
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.