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Subtract 3xy + 5yz – 7xz + 1 from -4xy + 2yz – 2xz + 5xyz + 1.
- a)5xz + 5xyz - 7xy - 3yz
- b)5xz + 5xyz + 7xy + 3yz
- c)-5xz + 5xyz - 7xy - 3yz
- d)-5xz + 5xyz + 7xy + 3yz
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Subtract 3xy + 5yz – 7xz + 1 from -4xy + 2yz – 2xz + 5xyz ...
Understanding the Problem
To solve the expression, we need to subtract the polynomial 3xy + 5yz - 7xz + 1 from the polynomial -4xy + 2yz - 2xz + 5xyz + 1.
Step 1: Write the Expressions
- Original expression: -4xy + 2yz - 2xz + 5xyz + 1
- Expression to subtract: 3xy + 5yz - 7xz + 1
Step 2: Set Up the Subtraction
This can be expressed as:
-4xy + 2yz - 2xz + 5xyz + 1 - (3xy + 5yz - 7xz + 1)
Step 3: Distribute the Negative Sign
When subtracting, distribute the negative sign:
= -4xy + 2yz - 2xz + 5xyz + 1 - 3xy - 5yz + 7xz - 1
Step 4: Combine Like Terms
Now, combine the like terms step-by-step:
1. xy Terms:
-4xy - 3xy = -7xy
2. yz Terms:
2yz - 5yz = -3yz
3. xz Terms:
-2xz + 7xz = 5xz
4. xyz Terms:
5xyz (only one term, remains as is)
5. Constant Terms:
1 - 1 = 0 (cancels out)
Final Expression
Putting all the combined terms together:
-7xy - 3yz + 5xz + 5xyz
Rearranging gives:
5xz + 5xyz - 7xy - 3yz
Conclusion
The final answer is:
5xz + 5xyz - 7xy - 3yz
This matches option (a), confirming that the correct answer is option 'A'.
To solve the expression, we need to subtract the polynomial 3xy + 5yz - 7xz + 1 from the polynomial -4xy + 2yz - 2xz + 5xyz + 1.
Step 1: Write the Expressions
- Original expression: -4xy + 2yz - 2xz + 5xyz + 1
- Expression to subtract: 3xy + 5yz - 7xz + 1
Step 2: Set Up the Subtraction
This can be expressed as:
-4xy + 2yz - 2xz + 5xyz + 1 - (3xy + 5yz - 7xz + 1)
Step 3: Distribute the Negative Sign
When subtracting, distribute the negative sign:
= -4xy + 2yz - 2xz + 5xyz + 1 - 3xy - 5yz + 7xz - 1
Step 4: Combine Like Terms
Now, combine the like terms step-by-step:
1. xy Terms:
-4xy - 3xy = -7xy
2. yz Terms:
2yz - 5yz = -3yz
3. xz Terms:
-2xz + 7xz = 5xz
4. xyz Terms:
5xyz (only one term, remains as is)
5. Constant Terms:
1 - 1 = 0 (cancels out)
Final Expression
Putting all the combined terms together:
-7xy - 3yz + 5xz + 5xyz
Rearranging gives:
5xz + 5xyz - 7xy - 3yz
Conclusion
The final answer is:
5xz + 5xyz - 7xy - 3yz
This matches option (a), confirming that the correct answer is option 'A'.
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Community Answer
Subtract 3xy + 5yz – 7xz + 1 from -4xy + 2yz – 2xz + 5xyz ...
We need to subtract (3xy + 5yz – 7xz + 1) from (-4xy + 2yz – 2xz + 5xyz + 1).
Step 1: Write the subtraction expression:
(-4xy + 2yz – 2xz + 5xyz + 1) - (3xy + 5yz – 7xz + 1)
Step 2: Distribute the minus sign across the second set of terms:
= -4xy + 2yz – 2xz + 5xyz + 1 - 3xy - 5yz + 7xz - 1
Step 3: Combine like terms:
- For xy terms: -4xy - 3xy = -7xy
- For yz terms: 2yz - 5yz = -3yz
- For xz terms: -2xz + 7xz = 5xz
- For xyz term: 5xyz (no like term)
- For constants: 1 - 1 = 0
Step 4: Write the final expression:
5xz + 5xyz - 7xy - 3yz
Thus, the correct answer is:
a) 5xz + 5xyz - 7xy - 3yz
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Question Description
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