Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.
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 visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.