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Answer :
To determine the terms in the expression [tex]\(5r - 4s - 2\)[/tex], we need to identify the individual components of the expression that are separated by plus or minus signs.
Here’s a step-by-step breakdown:
1. Identify the structure of the expression:
- The expression is [tex]\(5r - 4s - 2\)[/tex].
2. Break down the expression into individual terms:
- Terms are components of an expression that are added or subtracted.
- In this expression, it is helpful to think of it as [tex]\((+5r) + (-4s) + (-2)\)[/tex], since subtraction can be seen as adding a negative.
3. List the terms:
- First term: [tex]\(5r\)[/tex]
- Second term: [tex]\(-4s\)[/tex]
- Third term: [tex]\(-2\)[/tex]
From this breakdown, we identify the terms in the expression as:
- [tex]\(5r\)[/tex]
- [tex]\(-4s\)[/tex]
- [tex]\(-2\)[/tex]
Now, let's match these terms with the options provided:
- A. [tex]\(4s\)[/tex]: This is not a term in the expression because it has a positive sign whereas our term has a negative sign.
- B. [tex]\(-4s\)[/tex]: This is a term in the expression.
- C. [tex]\(5r - 4s\)[/tex]: This is not a term; it is part of the expression but not an individual term.
- D. [tex]\(-5r\)[/tex]: This is not a term in the expression; the term is [tex]\(5r\)[/tex] without a negative sign.
- E. [tex]\(5\)[/tex]: This is not a term; it is part of the term [tex]\(5r\)[/tex].
- F. [tex]\(-2\)[/tex]: This is a term in the expression.
Therefore, the terms in the expression [tex]\(5r - 4s - 2\)[/tex] are [tex]\(-4s\)[/tex] and [tex]\(-2\)[/tex]. Select options B and F.
Here’s a step-by-step breakdown:
1. Identify the structure of the expression:
- The expression is [tex]\(5r - 4s - 2\)[/tex].
2. Break down the expression into individual terms:
- Terms are components of an expression that are added or subtracted.
- In this expression, it is helpful to think of it as [tex]\((+5r) + (-4s) + (-2)\)[/tex], since subtraction can be seen as adding a negative.
3. List the terms:
- First term: [tex]\(5r\)[/tex]
- Second term: [tex]\(-4s\)[/tex]
- Third term: [tex]\(-2\)[/tex]
From this breakdown, we identify the terms in the expression as:
- [tex]\(5r\)[/tex]
- [tex]\(-4s\)[/tex]
- [tex]\(-2\)[/tex]
Now, let's match these terms with the options provided:
- A. [tex]\(4s\)[/tex]: This is not a term in the expression because it has a positive sign whereas our term has a negative sign.
- B. [tex]\(-4s\)[/tex]: This is a term in the expression.
- C. [tex]\(5r - 4s\)[/tex]: This is not a term; it is part of the expression but not an individual term.
- D. [tex]\(-5r\)[/tex]: This is not a term in the expression; the term is [tex]\(5r\)[/tex] without a negative sign.
- E. [tex]\(5\)[/tex]: This is not a term; it is part of the term [tex]\(5r\)[/tex].
- F. [tex]\(-2\)[/tex]: This is a term in the expression.
Therefore, the terms in the expression [tex]\(5r - 4s - 2\)[/tex] are [tex]\(-4s\)[/tex] and [tex]\(-2\)[/tex]. Select options B and F.
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