(x+8)(x+5)

2 min read Jun 17, 2024

Expanding (x + 8)(x + 5)

This article will walk through the steps of expanding the expression (x + 8)(x + 5).

Understanding the Problem

The expression (x + 8)(x + 5) represents the product of two binomials. Binomials are algebraic expressions with two terms. To expand the expression, we need to multiply each term in the first binomial by each term in the second binomial.

Using the FOIL Method

One common method for expanding 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.

Let's apply this to our expression:

F: x * x = x² O: x * 5 = 5x I: 8 * x = 8x L: 8 * 5 = 40

Now, we add all the terms together: x² + 5x + 8x + 40

Simplifying the Expression

Finally, we combine the like terms (the terms with 'x'): x² + 13x + 40

Conclusion

Therefore, the expanded form of (x + 8)(x + 5) is x² + 13x + 40.

This method can be applied to expanding any two binomials. Remember to multiply each term in the first binomial by each term in the second binomial, and then combine like terms to get the simplified expression.