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

2 min read Jun 16, 2024

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

This article will explain how to expand the expression (2x-3)(x+4), which is a product of two binomials. This process is often referred to as "FOIL" (First, Outer, Inner, Last) but can also be understood as a simple application of the distributive property.

Understanding the FOIL Method

The FOIL method is a mnemonic device used to remember the steps involved in multiplying two binomials:

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 FOIL to Our Expression

Let's apply the FOIL method to our expression (2x-3)(x+4):

First: (2x) * (x) = 2x²
Outer: (2x) * (4) = 8x
Inner: (-3) * (x) = -3x
Last: (-3) * (4) = -12

Now we have the following terms: 2x² + 8x - 3x - 12

Combining Like Terms

The final step is to combine like terms:

2x² + 5x - 12

Conclusion

Therefore, the expanded form of the expression (2x-3)(x+4) is 2x² + 5x - 12.

By following the FOIL method and combining like terms, we can successfully expand the expression and obtain its simplified form. This process is fundamental in algebra and is often used in solving equations and manipulating polynomials.