Math

QuestionIs John's simplification of the expression (x+y)+3(x4y)-(x+y)+3(x-4y) correct? Explain your reasoning.

Studdy Solution

STEP 1

Assumptions1. John's first step is to remove the parentheses in the expression. . John's second step is to combine like terms.

STEP 2

Let's follow John's first step and remove the parentheses in the expression. We can do this by distributing the negative sign to each term inside the parentheses.
(x+y)=xy-(x+y) = -x - y

STEP 3

Now, let's distribute the3 to each term inside the parentheses in the second part of the expression.
3(xy)=3x12y3(x-y) =3x -12y

STEP 4

So, the expression after removing the parentheses becomesxy+3x12y-x - y +3x -12y

STEP 5

Now, let's follow John's second step and combine like terms. We can do this by adding or subtracting the coefficients of the like terms.
Combining the x termsx+3x=2x-x +3x =2x

STEP 6

And combining the y termsy12y=13y-y -12y = -13y

STEP 7

So, the simplified expression becomes2x13y2x -13yJohn's simplified expression is 2x3y2x -3y, which is not the same as our simplified expression 2x13y2x -13y.
Therefore, John's work is not correct.

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