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Simplify the expression: [tex]4x(2y) + 3y(2 - x)[/tex]

A. [tex]11xy + 6y[/tex]
B. [tex]5xy + 6y[/tex]
C. [tex]8xy + 6y - x[/tex]
D. [tex]8xy + 6y - 3x[/tex]

Sagot :

GinnyAnswer
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]
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