If \(A=2 x-(y-2 c)\) and \(B=(2 x-y)-2 c,\) then \(A-B=\) a. \(-2 y\) b. \(-4 c\) c. \(-0\) d. \(-2 y\) e. \(-4 c\)

Short Answer

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Step by step solution

01

Substitute the values of A and B into A-B

To start, let’s input the given values of \(A\) and \(B\) into the expression \(A-B\). This gives us \((2x - (y - 2c)) - ((2x - y) - 2c)\)
02

Carry out the subtraction operation

Now, carefully subtract the expressions within the brackets. Recall rules of changing signs when subtracting expressions. This gives us \(2x - y + 2c - 2x + y - 2c\)
03

Simplify the resulting expression

Upon simplifying, we can clearly see that every term cancels each other out (positive 2x cancels negative 2x, negative y cancels positive y, positive 2c cancels negative 2c), leaving us with \(0\)

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