To simplify the expression \((x - 5)(x - 3)\), use the distributive property (also known as FOIL for binomials):

\[
(x - 5)(x - 3) = x(x - 3) - 5(x - 3)
\]

Now distribute each term:

\[
= x^2 - 3x - 5x + 15
\]

Combine like terms:

\[
x^2 - 8x + 15
\]

So, \((x - 5)(x - 3) = x^2 - 8x + 15\).

Would you like further details on this?

### Related Questions:
1. How do you factor \(x^2 - 8x + 15\)?
2. What are the roots of the equation \(x^2 - 8x + 15 = 0\)?
3. How does the distributive property apply to polynomials?
4. What is the FOIL method in binomial multiplication?
5. Can you use this process with other binomials like \((x - 4)(x - 2)\)?

**Tip**: Always group and combine like terms after distributing when multiplying polynomials!

Learn how to simplify the polynomial expression (x - 5)(x - 3) using the distributive property (FOIL method). This step-by-step guide covers essential algebraic concepts, making it perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation