To simplify the expression \((x-7)(x-3)\), we need to expand it using the distributive property, also known as the FOIL (First, Outer, Inner, Last) method for multiplying two binomials.

Here’s how we can expand it:

\[
(x-7)(x-3) = x \cdot x + x \cdot (-3) + (-7) \cdot x + (-7) \cdot (-3)
\]

Calculating each term:

1. **First**: \(x \cdot x = x^2\)
2. **Outer**: \(x \cdot (-3) = -3x\)
3. **Inner**: \((-7) \cdot x = -7x\)
4. **Last**: \((-7) \cdot (-3) = 21\)

Now, combine all these terms:

\[
x^2 - 3x - 7x + 21
\]

Combine like terms \((-3x - 7x)\):

\[
x^2 - 10x + 21
\]

So, the expanded form of \((x-7)(x-3)\) is:

\[
x^2 - 10x + 21
\]

Would you like more details or have any questions?

Here are some related questions to explore:

1. What is the factored form of the polynomial \(x^2 - 10x + 21\)?
2. How do you find the roots of the equation \(x^2 - 10x + 21 = 0\)?
3. What happens if you expand \((x+7)(x+3)\) instead?
4. Can you explain the difference between the distributive property and the FOIL method?
5. How do you use the quadratic formula to solve \(x^2 - 10x + 21 = 0\)?

**Tip**: When expanding binomials, always remember to multiply each term in the first binomial by each term in the second binomial.

Learn how to expand the binomial (x-7)(x-3) using the FOIL method with detailed steps and examples. This problem covers algebraic concepts such as binomial expansion and the FOIL method. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation