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Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).
- a)6x³ – x²y² – 2xy³
- b)5x³ – x²y² – 2xy³
- c)6x³ – 2x²y² – 2xy³
- d)6x³ – x²y² – 2xy²
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).a)6x³...
Step 1: Expand the Expression
To simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²), we start by expanding each part.
- First Term:
- x²(x – 3y²) = x³ – 3x²y²
- Second Term:
- –xy(y² – 2xy) = –xy² + 2x²y
- Third Term:
- –x(y³ – 5x²) = –xy³ + 5x³
Step 2: Combine the Expanded Terms
Now, we combine all the expanded terms:
- x³ – 3x²y² – xy² + 2x²y – xy³ + 5x³
Next, we group the like terms:
- Cubic Terms:
- x³ + 5x³ = 6x³
- Quadratic Terms:
- –3x²y² + 2x²y = –x²y²
- Linear Terms:
- –xy² – xy³ = –2xy³
Step 3: Final Simplification
Combining all these results gives us:
- Final Expression: 6x³ – x²y² – 2xy³
Conclusion
The simplified expression is indeed 6x³ – x²y² – 2xy³, which matches option 'A'. Thus, the correct answer is confirmed.
To simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²), we start by expanding each part.
- First Term:
- x²(x – 3y²) = x³ – 3x²y²
- Second Term:
- –xy(y² – 2xy) = –xy² + 2x²y
- Third Term:
- –x(y³ – 5x²) = –xy³ + 5x³
Step 2: Combine the Expanded Terms
Now, we combine all the expanded terms:
- x³ – 3x²y² – xy² + 2x²y – xy³ + 5x³
Next, we group the like terms:
- Cubic Terms:
- x³ + 5x³ = 6x³
- Quadratic Terms:
- –3x²y² + 2x²y = –x²y²
- Linear Terms:
- –xy² – xy³ = –2xy³
Step 3: Final Simplification
Combining all these results gives us:
- Final Expression: 6x³ – x²y² – 2xy³
Conclusion
The simplified expression is indeed 6x³ – x²y² – 2xy³, which matches option 'A'. Thus, the correct answer is confirmed.
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Community Answer
Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).a)6x³...
The simplified form of the expression is 6x³ – x²y² – 2xy³.
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Question Description
Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).a)6x³ – x²y² – 2xy³b)5x³ – x²y² – 2xy³c)6x³ – 2x²y² – 2xy³d)6x³ – x²y² – 2xy²Correct answer is option 'A'. Can you explain this answer? for Class 8 2026 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).a)6x³ – x²y² – 2xy³b)5x³ – x²y² – 2xy³c)6x³ – 2x²y² – 2xy³d)6x³ – x²y² – 2xy²Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 8 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Simplify the expression x²(x – 3y²) – xy(y² – 2xy) – x(y³ – 5x²).a)6x³ – x²y² – 2xy³b)5x³ – x²y² – 2xy³c)6x³ – 2x²y² – 2xy³d)6x³ – x²y² – 2xy²Correct answer is option 'A'. Can you explain this answer?.
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