To expand the expression \((a + 1)(a + 2)\), we use the distributive property (also known as the FOIL method for binomials). Here’s the step-by-step process:

1. **First**: Multiply the first terms in each binomial: \(a \cdot a = a^2\).
2. **Outer**: Multiply the outer terms in the binomials: \(a \cdot 2 = 2a\).
3. **Inner**: Multiply the inner terms in the binomials: \(1 \cdot a = a\).
4. **Last**: Multiply the last terms in each binomial: \(1 \cdot 2 = 2\).

Now, add all these products together:
\[ a^2 + 2a + a + 2 \]

Combine like terms:
\[ a^2 + 3a + 2 \]

So, the expanded form of \((a + 1)(a + 2)\) is:
\[ a^2 + 3a + 2 \]

Would you like any further details or have any questions?

Here are 5 more questions you might be interested in:

1. How do you solve quadratic equations?
2. Can you explain the difference between permutations and combinations?
3. What is the derivative of \( \sin(x) \)?
4. How do you integrate \( x^2 \)?
5. What are the properties of logarithms?

**Tip:** When expanding binomials, always remember the FOIL method (First, Outer, Inner, Last) for an easy and systematic approach.

Learn how to expand the expression (a + 1)(a + 2) using the FOIL method step-by-step. This problem covers key algebraic concepts including binomial expansion and the FOIL method. Suitable for students in Grades 7-9.

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