(2x + 7)(x – 5)

2 min read Jun 16, 2024

Expanding the Expression (2x + 7)(x – 5)

This article will demonstrate how to expand the expression (2x + 7)(x – 5) using the FOIL method.

Understanding the FOIL Method

FOIL stands for First, Outer, Inner, Last. This acronym helps us remember the order in which to multiply the terms in two binomials. Let's break it down:

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

Applying the FOIL Method

First: (2x) * (x) = 2x²
Outer: (2x) * (-5) = -10x
Inner: (7) * (x) = 7x
Last: (7) * (-5) = -35

Combining Like Terms

Now, we combine the terms we obtained from the FOIL method:

2x² - 10x + 7x - 35

This simplifies to:

2x² - 3x - 35

Conclusion

Therefore, the expanded form of (2x + 7)(x – 5) is 2x² - 3x - 35. This method can be applied to any two binomials you encounter.