At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
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]
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]
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.