(4x+3)(2x-1)

2 min read Jun 16, 2024

Expanding the Expression: (4x + 3)(2x - 1)

This article will guide you through the process of expanding the expression (4x + 3)(2x - 1).

Understanding the Problem

The expression (4x + 3)(2x - 1) represents the product of two binomials. To expand this, we need to multiply each term in the first binomial by each term in the second binomial.

The FOIL Method

A common technique to expand binomials is the FOIL method. FOIL stands for:

First: Multiply the first terms of each binomial.
Outer: Multiply the outer terms of the binomials.
Inner: Multiply the inner terms of the binomials.
Last: Multiply the last terms of each binomial.

Applying the FOIL Method

Let's apply the FOIL method to our expression:

First: (4x)(2x) = 8x²
Outer: (4x)(-1) = -4x
Inner: (3)(2x) = 6x
Last: (3)(-1) = -3

Now, we combine the terms:

8x² - 4x + 6x - 3

Simplifying the Expression

Finally, we simplify by combining the like terms:

8x² + 2x - 3

Conclusion

Therefore, the expanded form of (4x + 3)(2x - 1) is 8x² + 2x - 3. The FOIL method provides a systematic way to expand binomials, ensuring that all terms are properly multiplied.