Let's simplify the given expression [tex]\(3 x^2(a-2) - 6 x(a-2)\)[/tex] step by step.
1. Identify the common factor:
Notice that both terms in the expression have a common factor of [tex]\((a-2)\)[/tex]. This common factor can be factored out of the expression.
2. Factor out the common term:
When we factor out [tex]\((a-2)\)[/tex], we get:
[tex]\[
3 x^2(a-2) - 6 x(a-2) = (a-2) [3 x^2 - 6 x]
\][/tex]
3. Simplify the expression inside the bracket:
We can further simplify the expression inside the bracket. To do this, we see if there is a common factor in [tex]\(3 x^2 - 6 x\)[/tex]:
[tex]\[
3x^2 - 6x
\][/tex]
Notice that both terms [tex]\(3x^2\)[/tex] and [tex]\(-6x\)[/tex] have a common factor of [tex]\(3x\)[/tex].
4. Factor out [tex]\(3x\)[/tex] from the expression inside the bracket:
[tex]\[
3x^2 - 6x = 3x(x - 2)
\][/tex]
5. Combine everything:
Substitute [tex]\(3x(x - 2)\)[/tex] back into the factored expression:
[tex]\[
(a-2) [3 x (x - 2)]
\][/tex]
So, the simplified expression is:
[tex]\[
3 x^2(a-2) - 6 x(a-2) = (a-2) [3 x (x - 2)]
\][/tex]
Thus, the final answer is:
[tex]\[
3 x^2(a-2) - 6 x(a-2) = (a-2) \cdot 3x \cdot (x - 2)
\][/tex]
