To evaluate \( G(a - 2) \) using the function \( G(x) = x^2 + 5x \), you need to substitute \( a - 2 \) for \( x \) in the expression.

So:

\[
G(a - 2) = (a - 2)^2 + 5(a - 2)
\]

Now, let's simplify this step-by-step:

### Step 1: Expand \( (a - 2)^2 \)
\[
(a - 2)^2 = a^2 - 4a + 4
\]

### Step 2: Distribute the 5 in \( 5(a - 2) \)
\[
5(a - 2) = 5a - 10
\]

### Step 3: Add the two expressions together
\[
G(a - 2) = a^2 - 4a + 4 + 5a - 10
\]

### Step 4: Combine like terms
\[
G(a - 2) = a^2 + (5a - 4a) + (4 - 10)
\]
\[
G(a - 2) = a^2 + a - 6
\]

So, the simplified expression is:

\[
G(a - 2) = a^2 + a - 6
\]

Would you like further explanation or have any questions about this?

### Related questions:
1. How do you expand binomials like \( (a - 2)^2 \)?
2. Can you explain how to distribute terms in expressions?
3. What are like terms, and how do you combine them?
4. How does evaluating functions at different inputs work?
5. How does this process change if \( a \) is a specific number instead of a variable?

**Tip:** Always ensure you fully expand and simplify expressions when evaluating functions!

Learn how to evaluate and simplify the function G(a - 2) for G(x) = x^2 + 5x. This detailed step-by-step solution covers key algebraic concepts such as function evaluation, binomial expansion, and combining like terms. Ideal for students in Grades 8-10.

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