To expand the expression \((x + 5)(x + 2)\), use the distributive property (also known as the FOIL method for binomials):

1. **First:** \(x \cdot x = x^2\)  
2. **Outer:** \(x \cdot 2 = 2x\)  
3. **Inner:** \(5 \cdot x = 5x\)  
4. **Last:** \(5 \cdot 2 = 10\)  

Now, add these terms together:
\[
x^2 + 2x + 5x + 10
\]

Combine like terms (\(2x + 5x\)) to get:
\[
x^2 + 7x + 10
\]

Therefore, the expanded form is:
\[
x^2 + 7x + 10
\]

Would you like more details or have any questions?

Here are some related questions to deepen your understanding:
1. How would you expand \((x + 3)(x + 4)\)?
2. Can you factor the expression \(x^2 + 7x + 10\) back into its original form?
3. How would the expansion change if the expression was \((x + 5)(x - 2)\)?
4. What is the significance of the coefficients in the expanded form?
5. How can you apply this expansion technique to solve quadratic equations?

**Tip:** When expanding binomials, always make sure to combine like terms for a simplified final expression.

Learn how to expand and simplify the expression (x+5)(x+2) using the FOIL method. This algebra problem involves polynomial expansion and combining like terms, suitable for students in Grades 8-10. Step-by-step solution included.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation