To solve the problem of subtracting [tex]\( 3x(x - 2y) \)[/tex] from [tex]\( 6(x^2 - xy) \)[/tex] and expressing the answer as a monomial, follow these steps:
1. Expand the expressions:
First, let's expand both expressions:
[tex]\[
6(x^2 - xy) = 6x^2 - 6xy
\][/tex]
[tex]\[
3x(x - 2y) = 3x^2 - 6xy
\][/tex]
2. Set up the subtraction:
We need to subtract [tex]\( 3x(x - 2y) \)[/tex] from [tex]\( 6(x^2 - xy) \)[/tex]. So we set up the expression as:
[tex]\[
(6x^2 - 6xy) - (3x^2 - 6xy)
\][/tex]
3. Combine like terms:
When subtracting, distribute the negative sign across the terms inside the parentheses:
[tex]\[
6x^2 - 6xy - 3x^2 + 6xy
\][/tex]
Next, combine the like terms:
[tex]\[
(6x^2 - 3x^2) + (-6xy + 6xy)
\][/tex]
Simplify the expressions:
[tex]\[
3x^2 + 0
\][/tex]
4. Express the answer as a monomial:
The result simplifies directly to a single term:
[tex]\[
3x^2
\][/tex]
Therefore, the answer, expressed as a monomial, is [tex]\( \boxed{3x^2} \)[/tex].
