Problem 21 - College Algebra Essentials

Question

Find each product. $$(x-5)(x+3)$$

Step-by-Step Solution

Answer

The product of the binomials \( (x-5) \) and \( (x+3) \) is \( x^2 - 2x - 15 \).

Step 1: Apply the distributive property

Firstly, distribute each term in binomial \( (x-5) \) by all terms in \( (x+3) \). The multiplication should look like this: \(x * x + x * 3 - 5 * x - 5 * 3\). This is done by taking each term of the first binomial and multiplying it individually by each term of the second binomial.

Step 2: Simplify the multiplication

Next, simplify all the multiplication expressions obtained after distribution: \(x^2 + 3x - 5x - 15\).

Step 3: Combine like terms

The final step is to combine like terms. In this case, the terms containing \(x\) can be combined. This simplifies to: \(x^2 - 2x - 15\).