Sure, let's simplify the expression step-by-step:
1. Write down the original expression:
[tex]\[
12x^2 y - 9xy + 6xy^2 + 6y - 3xy
\][/tex]
2. Combine like terms:
Notice that [tex]\( -9xy \)[/tex] and [tex]\( -3xy \)[/tex] can be combined as they are like terms. So, we'll rewrite the expression:
[tex]\[
12x^2 y + 6xy^2 + 6y - 12xy
\][/tex]
3. Identify common factors:
In the expression, we can factor out common terms. Look at each term and recognize the common factors.
4. Factor out common terms:
[tex]\[
= 6y \left(2x^2 + x y - 2x + 1\right)
\][/tex]
So, the expression [tex]\( 12x^2 y - 9xy + 6xy^2 + 6y - 3xy \)[/tex] simplifies to:
[tex]\[
6y(2x^2 + xy - 2x + 1)
\][/tex]
