(2x-1)(3x+4)=ax^2+bx+c

3 min read Jun 16, 2024

Expanding and Simplifying Quadratic Expressions: (2x-1)(3x+4) = ax^2 + bx + c

This article will explore the process of expanding and simplifying a quadratic expression, specifically focusing on the example: (2x-1)(3x+4) = ax^2 + bx + c.

Understanding the Problem

The equation (2x-1)(3x+4) = ax^2 + bx + c presents us with a product of two binomials on the left side and a standard quadratic expression on the right side. The goal is to expand the left side and then compare the coefficients to find the values of a, b, and c.

Expanding the Left Side

To expand the product of the two binomials, we can use the FOIL method (First, Outer, Inner, Last):

First: Multiply the first terms of each binomial: (2x)(3x) = 6x^2
Outer: Multiply the outer terms: (2x)(4) = 8x
Inner: Multiply the inner terms: (-1)(3x) = -3x
Last: Multiply the last terms: (-1)(4) = -4

Now, combine the terms: 6x^2 + 8x - 3x - 4 = 6x^2 + 5x - 4

Comparing Coefficients

We have now expanded the left side of the equation: 6x^2 + 5x - 4 = ax^2 + bx + c

By comparing the coefficients of both sides, we can identify the values of a, b, and c:

a = 6 (coefficient of x^2)
b = 5 (coefficient of x)
c = -4 (constant term)

Conclusion

Therefore, by expanding and simplifying the given expression, we have found that a = 6, b = 5, and c = -4. This demonstrates how to manipulate algebraic expressions and solve for unknown coefficients.