Certainly! Let's simplify the given algebraic expression step by step.
Given expression:
[tex]\[ -12xy + 3x^2 - x(3 - 5y) + 3xy \][/tex]
Step 1: Distribute and combine like terms
First, distribute [tex]\( x \)[/tex] through the expression inside the parentheses:
[tex]\[ -12xy + 3x^2 - x \cdot 3 + x \cdot 5y + 3xy \][/tex]
[tex]\[ -12xy + 3x^2 - 3x + 5xy + 3xy \][/tex]
Next, combine the like terms involving [tex]\( xy \)[/tex]:
[tex]\[ -12xy + 5xy + 3xy = -12xy + 8xy = -4xy \][/tex]
So, the expression now is:
[tex]\[ 3x^2 - 3x - 4xy \][/tex]
Step 2: Factor the expression if possible
We can factor out a common factor [tex]\( x \)[/tex] from each term:
[tex]\[ x(3x - 3 - 4y) \][/tex]
So, the simplified form of the given expression is:
[tex]\[ x(3x - 3 - 4y) \][/tex]
Thus, the final simplified expression is:
[tex]\[ x(3x - 4y - 3) \][/tex]
So, the original expression [tex]\( -12xy + 3x^2 - x(3 - 5y) + 3xy \)[/tex] simplifies to:
[tex]\[ x(3x - 4y - 3) \][/tex]
