Certainly! Let's simplify and rewrite the expression [tex]\(4 x z - 12 x y\)[/tex]. Here's a step-by-step breakdown:
1. Identify Common Factors:
- Both terms in the expression [tex]\(4 x z\)[/tex] and [tex]\(-12 x y\)[/tex] have a common factor of [tex]\(x\)[/tex].
2. Factor Out the Common Factor:
- The common factor is [tex]\(x\)[/tex]. So, we factor out [tex]\(x\)[/tex] from both terms.
[tex]\[
x (4z - 12y)
\][/tex]
3. Rewrite the Expression:
- The factored form of the expression [tex]\(4 x z - 12 x y\)[/tex] is [tex]\(x (4z - 12y)\)[/tex].
4. Verify the Simplification (By Distribution):
- If we distribute [tex]\(x\)[/tex] back into each term inside the parentheses, we should get back the original expression.
[tex]\[
x \cdot 4z = 4xz \quad \text{and} \quad x \cdot -12y = -12xy
\][/tex]
- Therefore, [tex]\(x (4z - 12y) = 4 x z - 12 x y\)[/tex].
After these steps, the expression [tex]\(4 x z - 12 x y\)[/tex] can be factorized and simplified as [tex]\(x (4z - 12y)\)[/tex]. The simplified expression is consistent with our distribution check, ensuring that no mistake was made during the factoring process.
So, the simplified form of the given expression is:
[tex]\[
-12xy + 4xz
\][/tex]
