Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine which terms result in a monomial when added to [tex]\(3x^2y\)[/tex], we need to ensure that the resulting expression is a single term with matching variable parts and exponents.
Consider the given terms to be added to [tex]\(3x^2y\)[/tex]:
1. [tex]\(3xy\)[/tex]
2. [tex]\(-12x^2y\)[/tex]
3. [tex]\(2x^2y^2\)[/tex]
4. [tex]\(7xy^2\)[/tex]
5. [tex]\(-10x^2\)[/tex]
6. [tex]\(4x^2y\)[/tex]
7. [tex]\(3x^3\)[/tex]
### Step-by-Step Analysis:
1. [tex]\(3xy\)[/tex]:
- The term [tex]\(3xy\)[/tex] has the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], but the exponents do not match [tex]\(3x^2y\)[/tex] (which should have [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex]).
- Result after addition: [tex]\(3x^2y + 3xy\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
2. [tex]\(-12x^2y\)[/tex]:
- The term [tex]\(-12x^2y\)[/tex] has the exact same variables [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex] as [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y - 12x^2y = -9x^2y\)[/tex]
- This is a single term (monomial).
3. [tex]\(2x^2y^2\)[/tex]:
- The term [tex]\(2x^2y^2\)[/tex] has [tex]\(x^2\)[/tex] and [tex]\(y^2\)[/tex], not matching [tex]\(3x^2y\)[/tex] (which only has [tex]\(y\)[/tex]).
- Result after addition: [tex]\(3x^2y + 2x^2y^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
4. [tex]\(7xy^2\)[/tex]:
- The term [tex]\(7xy^2\)[/tex] has the variables [tex]\(x\)[/tex] and [tex]\(y^2\)[/tex], not matching [tex]\(3x^2y\)[/tex] (which should have [tex]\(x^2\)[/tex]).
- Result after addition: [tex]\(3x^2y + 7xy^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
5. [tex]\(-10x^2\)[/tex]:
- The term [tex]\(-10x^2\)[/tex] lacks the variable [tex]\(y\)[/tex] entirely.
- Result after addition: [tex]\(3x^2y - 10x^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing variables.
6. [tex]\(4x^2y\)[/tex]:
- The term [tex]\(4x^2y\)[/tex] has the exact same variables [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex] as [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y + 4x^2y = 7x^2y\)[/tex]
- This is a single term (monomial).
7. [tex]\(3x^3\)[/tex]:
- The term [tex]\(3x^3\)[/tex] has [tex]\(x^3\)[/tex] instead of [tex]\(x^2\)[/tex], not matching [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y + 3x^3\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
### Conclusion:
The terms that would result in a monomial when added to [tex]\(3x^2y\)[/tex] are:
- [tex]\(-12x^2y\)[/tex]
- [tex]\(4x^2y\)[/tex]
So, the correct answers are:
- [tex]\(-12 x^2 y\)[/tex]
- [tex]\(4 x^2 y\)[/tex]
Consider the given terms to be added to [tex]\(3x^2y\)[/tex]:
1. [tex]\(3xy\)[/tex]
2. [tex]\(-12x^2y\)[/tex]
3. [tex]\(2x^2y^2\)[/tex]
4. [tex]\(7xy^2\)[/tex]
5. [tex]\(-10x^2\)[/tex]
6. [tex]\(4x^2y\)[/tex]
7. [tex]\(3x^3\)[/tex]
### Step-by-Step Analysis:
1. [tex]\(3xy\)[/tex]:
- The term [tex]\(3xy\)[/tex] has the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex], but the exponents do not match [tex]\(3x^2y\)[/tex] (which should have [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex]).
- Result after addition: [tex]\(3x^2y + 3xy\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
2. [tex]\(-12x^2y\)[/tex]:
- The term [tex]\(-12x^2y\)[/tex] has the exact same variables [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex] as [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y - 12x^2y = -9x^2y\)[/tex]
- This is a single term (monomial).
3. [tex]\(2x^2y^2\)[/tex]:
- The term [tex]\(2x^2y^2\)[/tex] has [tex]\(x^2\)[/tex] and [tex]\(y^2\)[/tex], not matching [tex]\(3x^2y\)[/tex] (which only has [tex]\(y\)[/tex]).
- Result after addition: [tex]\(3x^2y + 2x^2y^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
4. [tex]\(7xy^2\)[/tex]:
- The term [tex]\(7xy^2\)[/tex] has the variables [tex]\(x\)[/tex] and [tex]\(y^2\)[/tex], not matching [tex]\(3x^2y\)[/tex] (which should have [tex]\(x^2\)[/tex]).
- Result after addition: [tex]\(3x^2y + 7xy^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
5. [tex]\(-10x^2\)[/tex]:
- The term [tex]\(-10x^2\)[/tex] lacks the variable [tex]\(y\)[/tex] entirely.
- Result after addition: [tex]\(3x^2y - 10x^2\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing variables.
6. [tex]\(4x^2y\)[/tex]:
- The term [tex]\(4x^2y\)[/tex] has the exact same variables [tex]\(x^2\)[/tex] and [tex]\(y\)[/tex] as [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y + 4x^2y = 7x^2y\)[/tex]
- This is a single term (monomial).
7. [tex]\(3x^3\)[/tex]:
- The term [tex]\(3x^3\)[/tex] has [tex]\(x^3\)[/tex] instead of [tex]\(x^2\)[/tex], not matching [tex]\(3x^2y\)[/tex].
- Result after addition: [tex]\(3x^2y + 3x^3\)[/tex]
- This results into a polynomial, not a monomial, because the terms cannot be combined into a single term due to differing exponents.
### Conclusion:
The terms that would result in a monomial when added to [tex]\(3x^2y\)[/tex] are:
- [tex]\(-12x^2y\)[/tex]
- [tex]\(4x^2y\)[/tex]
So, the correct answers are:
- [tex]\(-12 x^2 y\)[/tex]
- [tex]\(4 x^2 y\)[/tex]
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We appreciate your time. Please come back anytime for the latest information and answers to your questions. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.
