Sure! Let's simplify the given expression step-by-step:
The expression to simplify is:
[tex]\[ 4x(2y) + 3y(2 - x) - (8xy + 6y - 3x) \][/tex]
### Step 1: Distribute the terms inside the parentheses
First, distribute the terms in the expressions:
[tex]\[ 4x(2y) = 8xy \][/tex]
[tex]\[ 3y(2 - x) = 3y \cdot 2 - 3y \cdot x = 6y - 3xy \][/tex]
And keep the terms inside the parentheses:
[tex]\[ 8xy + 6y - 3x \][/tex]
So the expression now becomes:
[tex]\[ 8xy + 6y - 3xy - (8xy + 6y - 3x) \][/tex]
### Step 2: Distribute the negative sign across the parentheses
Distribute the negative sign across the terms in the parentheses:
[tex]\[ -(8xy + 6y - 3x) = -8xy - 6y + 3x \][/tex]
Thus, the expression becomes:
[tex]\[ 8xy + 6y - 3xy - 8xy - 6y + 3x \][/tex]
### Step 3: Combine like terms
Combine the like terms:
- Combine the [tex]\( xy \)[/tex] terms: [tex]\( 8xy - 3xy - 8xy = -3xy \)[/tex]
- Combine the [tex]\( y \)[/tex] terms: [tex]\( 6y - 6y = 0 \)[/tex]
- Combine the [tex]\( x \)[/tex] term: just [tex]\( +3x \)[/tex]
So, we are left with:
[tex]\[ -3xy + 3x \][/tex]
### Step 4: Factor out the common terms
Factor out the common factor from the terms:
[tex]\[ -3xy + 3x = 3x(1 - y) \][/tex]
### Final Simplified Expression
The simplified expression is:
[tex]\[ 3x(1 - y) \][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[ 3x(1 - y) \][/tex]
