Questions: 2x-3[2(x-y)+4x]= (A) -16x+y (B) -16x+6y (C) 16x-y

2x-3[2(x-y)+4x]= (A) -16x+y (B) -16x+6y (C) 16x-y
Transcript text: \[ 2 x-3[2(x-y)+4 x]= \] (A) $-16 x+y$ (B) $-16 x+6 y$ (C) $16 x-y$
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Solution

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Solution Steps

Step 1: Expand the inner expression

First, expand the inner expression \(2(x - y)\): \[ 2(x - y) = 2x - 2y. \]

Step 2: Substitute and simplify

Substitute \(2(x - y)\) back into the original expression: \[ 2x - 3[2(x - y) + 4x] = 2x - 3[(2x - 2y) + 4x]. \] Simplify the expression inside the brackets: \[ (2x - 2y) + 4x = 6x - 2y. \]

Step 3: Distribute the \(-3\)

Now distribute \(-3\) across the simplified expression: \[ 2x - 3(6x - 2y) = 2x - 18x + 6y. \]

Step 4: Combine like terms

Combine the like terms: \[ 2x - 18x + 6y = -16x + 6y. \]

Final Answer

The simplified expression is: \[ \boxed{-16x + 6y}. \] The correct choice is B.

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