Consider the expression 
3
x
 − 
6
x + 3
 − 
x
(x + 3)2
 .
(a)
How many terms does this expression have?

Let's analyze the given expression step by step:

\[
3x - 6x + 3 - x(x + 3)^2
\]

### Breaking it down:
1. \( 3x \) is the first term.
2. \( -6x \) is the second term.
3. \( 3 \) is the third term.
4. \( -x(x + 3)^2 \) is the fourth term.

The expression consists of four distinct terms.

Thus, the expression has **4 terms**.

Would you like a detailed breakdown of how to simplify this expression further, or have any other questions?

### Related Questions:
1. How can we simplify the expression \( 3x - 6x + 3 - x(x + 3)^2 \)?
2. What is the degree of the term \( -x(x + 3)^2 \)?
3. What happens if we factor the expression \( 3x - 6x + 3 \)?
4. How does expanding \( (x + 3)^2 \) affect the complexity of the expression?
5. Can this expression be simplified into a quadratic form?

### Tip:
Always distribute and combine like terms when simplifying expressions to reduce the number of terms.

Consider the expression 3x − 6x + 3 − x(x + 3)^2. (a) How many terms does this expression have?

This article explains how to count terms in the expression 3x - 6x + 3 - x(x + 3)^2 by breaking it down step by step. Learn about key algebraic concepts such as distribution and combining like terms, suitable for students in Grades 9-12.

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