(2x+5)(x-3) Answer

2 min read Jun 16, 2024

Expanding the Expression (2x + 5)(x - 3)

This article explores how to expand the expression (2x + 5)(x - 3). This process is commonly known as multiplying binomials.

Understanding the Process

To expand the expression, we need to distribute each term in the first binomial to each term in the second binomial. This can be achieved using the FOIL method:

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

Let's apply FOIL to our expression (2x + 5)(x - 3):

First: (2x)(x) = 2x²
Outer: (2x)(-3) = -6x
Inner: (5)(x) = 5x
Last: (5)(-3) = -15

Combining Like Terms

Now, we have the expanded expression: 2x² - 6x + 5x - 15. Combining the like terms (-6x + 5x), we get:

2x² - x - 15

Conclusion

Therefore, the expanded form of the expression (2x + 5)(x - 3) is 2x² - x - 15. This process demonstrates the importance of applying the distributive property and combining like terms to simplify expressions.