Problem 21 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of (x - 5)(x + 3) is \( x^2 - 2x - 15 \)

Step 1: Expand using Distributive Property

To perform the multiplication, we use the distributive property, often recalled with the acronym FOIL. Thus, to find the product (x - 5)(x + 3) use FOIL which stands for: Multiply the First terms, then the Outside terms, the Inside and finally the Last terms. Expanding gives: \( x*x + x*3 + -5*x + -5*3 \)

Step 2: Perform Multiplications

Now, perform the multiplications: \( x^2 + 3x - 5x - 15 \)

Step 3: Combine Like Terms

Finally, look for and combine 'like' terms: \( x^2 - 2x - 15 \)