fully factorise by first taking out the highest common factor: 3(x-2)-x(x-2)

Let's fully factorize the expression \( 3(x - 2) - x(x - 2) \).

### Step-by-Step Solution:

1. **Identify the common factor**:  
   Notice that both terms in the expression contain \( (x - 2) \) as a factor. Therefore, we can factor out \( (x - 2) \) from the entire expression.
   \[
   3(x - 2) - x(x - 2) = (x - 2)(3 - x)
   \]

2. **Simplify further (optional)**:  
   The expression \( (3 - x) \) can also be written as \( -(x - 3) \). So, we can rewrite the expression as:
   \[
   (x - 2)(3 - x) = -(x - 2)(x - 3)
   \]

Thus, the fully factorized form of the expression is:
\[
-(x - 2)(x - 3)
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Factorize \( 4(x - 5) - 2(x - 5) \).
2. Factorize \( 2x(x + 1) - 3(x + 1) \).
3. Factorize \( 5(x - 3) + 7(x - 3) \).
4. Factorize \( 6x(x + 2) - 4x(x + 2) \).
5. Factorize \( x^2 - 5x + 6 \).

**Tip:** Always look for common factors before applying other factoring techniques like grouping or the quadratic formula.

Discover how to fully factor the algebraic expression 3(x - 2) - x(x - 2) by identifying the highest common factor and using the distributive property. This step-by-step solution is ideal for students in Grades 8-10 learning algebraic factoring techniques.

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