QuestionIdentify the wrong description of the expression $2(x+y)$ from the options: a, b, c, or d.

Studdy Solution

STEP 1

Assumptions1. The mathematical expression is $(x+y)$ . We need to find the incorrect description of this expression

STEP 2

Let's examine each choice one by one.a. twice the sum of $x$ and $y$ .
This is a correct description of the expression $2(x+y)$ . When we say "twice the sum of $x$ and $y$ ", it means we add $x$ and $y$ together, and then multiply the result by2. This is exactly what the expression $2(x+y)$ represents.

STEP 3

b. the sum of twice $x$ and $y$ .
This description would correspond to the expression $2x + y$ , not $2(x+y)$ . In the expression $2x + y$ , we are multiplying $x$ by2, and then adding $y$ . This is different from $2(x+y)$ , where we first add $x$ and $y$ together, and then multiply the result by2. Therefore, this is an incorrect description of the expression $2(x+y)$ .

STEP 4

c. the sum of twice $x$ and twice $y$ .
This description would correspond to the expression $2x +2y$ , which is equivalent to $2(x+y)$ . When we say "the sum of twice $x$ and twice $y$ ", it means we multiply $x$ by2, multiply $y$ by2, and then add the results together. This is exactly what the expression $2(x+y)$ represents when it is expanded.

STEP 5

d. the product of2 and the sum of $x$ and $y$ .
This is a correct description of the expression $2(x+y)$ . When we say "the product of2 and the sum of $x$ and $y$ ", it means we add $x$ and $y$ together, and then multiply the result by2. This is exactly what the expression $2(x+y)$ represents.
The incorrect description of the mathematical expression $2(x+y)$ isb. the sum of twice $x$ and $y$ .

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