Answer :
To find the simplest form of the given algebraic expression [tex]\(- (6x + 2y) + 4(2x - y)\)[/tex], let's proceed step-by-step:
1. Distribute the negative sign and the 4 across the terms inside the parentheses:
- For [tex]\(- (6x + 2y)\)[/tex], distribute the [tex]\(-\)[/tex] sign through the terms inside the parentheses:
[tex]\[ - (6x + 2y) = -6x - 2y \][/tex]
- For [tex]\(4 (2x - y)\)[/tex], distribute the 4 through the terms inside the parentheses:
[tex]\[ 4 (2x - y) = 4 \cdot 2x - 4 \cdot y = 8x - 4y \][/tex]
2. Combine like terms from the results of the distribution:
- The expression now is:
[tex]\[ -6x - 2y + 8x - 4y \][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -6x + 8x = 2x \][/tex]
- Combine the [tex]\(y\)[/tex] terms:
[tex]\[ -2y - 4y = -6y \][/tex]
3. Write the final simplified form of the expression:
[tex]\[ 2x - 6y \][/tex]
So, the simplest form of the expression [tex]\( - (6x + 2y) + 4(2x - y) \)[/tex] is [tex]\( 2x - 6y \)[/tex].
The correct answer is:
C. [tex]\(2x - 6y\)[/tex]
1. Distribute the negative sign and the 4 across the terms inside the parentheses:
- For [tex]\(- (6x + 2y)\)[/tex], distribute the [tex]\(-\)[/tex] sign through the terms inside the parentheses:
[tex]\[ - (6x + 2y) = -6x - 2y \][/tex]
- For [tex]\(4 (2x - y)\)[/tex], distribute the 4 through the terms inside the parentheses:
[tex]\[ 4 (2x - y) = 4 \cdot 2x - 4 \cdot y = 8x - 4y \][/tex]
2. Combine like terms from the results of the distribution:
- The expression now is:
[tex]\[ -6x - 2y + 8x - 4y \][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[ -6x + 8x = 2x \][/tex]
- Combine the [tex]\(y\)[/tex] terms:
[tex]\[ -2y - 4y = -6y \][/tex]
3. Write the final simplified form of the expression:
[tex]\[ 2x - 6y \][/tex]
So, the simplest form of the expression [tex]\( - (6x + 2y) + 4(2x - y) \)[/tex] is [tex]\( 2x - 6y \)[/tex].
The correct answer is:
C. [tex]\(2x - 6y\)[/tex]
