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What are the factors of x4+y4+x2y2?
- a)(x2+y2) and (x2+y2−xy)
- b)(x2+y2)and (x2−y2)
- c)(x2+y2+xy) and (x2+y2−xy)
- d)Factorization is not possibl
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y...
x4+y4+x2y2 =(x4+y4+2x2y2)−x2y2 =(x2+y2)2−(xy)2
=(x2+y2+xy)(x2+y2−xy)
=(x2+y2+xy)(x2+y2−xy)
Most Upvoted Answer
What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y...
Understanding the Expression
To factor the expression x^4 + y^4 + x^2y^2, we will look for patterns and identities that help in simplifying it.
Identifying the Structure
1. The expression can be rewritten as:
- (x^2)^2 + (y^2)^2 + (x^2y^2)
2. This resembles a form that can be factored using the sum of squares and products.
Using the Factorization Formula
1. We can use the identity for the sum of squares:
- a^2 + b^2 + c^2 = (a + b + c)(a + b - c) when a, b, and c are expressions.
2. In our case, let:
- a = x^2
- b = y^2
- c = xy
3. Thus, we can express it as:
- (x^2 + y^2 + xy)(x^2 + y^2 - xy)
Proof of Factorization
1. To verify:
- Multiply (x^2 + y^2 + xy) and (x^2 + y^2 - xy).
- Distributing gives:
- x^4 + y^4 + x^2y^2, confirming our factorization.
Conclusion
The correct factors of x^4 + y^4 + x^2y^2 are indeed:
- (x^2 + y^2 + xy) and (x^2 + y^2 - xy).
Therefore, option 'C' is correct.
To factor the expression x^4 + y^4 + x^2y^2, we will look for patterns and identities that help in simplifying it.
Identifying the Structure
1. The expression can be rewritten as:
- (x^2)^2 + (y^2)^2 + (x^2y^2)
2. This resembles a form that can be factored using the sum of squares and products.
Using the Factorization Formula
1. We can use the identity for the sum of squares:
- a^2 + b^2 + c^2 = (a + b + c)(a + b - c) when a, b, and c are expressions.
2. In our case, let:
- a = x^2
- b = y^2
- c = xy
3. Thus, we can express it as:
- (x^2 + y^2 + xy)(x^2 + y^2 - xy)
Proof of Factorization
1. To verify:
- Multiply (x^2 + y^2 + xy) and (x^2 + y^2 - xy).
- Distributing gives:
- x^4 + y^4 + x^2y^2, confirming our factorization.
Conclusion
The correct factors of x^4 + y^4 + x^2y^2 are indeed:
- (x^2 + y^2 + xy) and (x^2 + y^2 - xy).
Therefore, option 'C' is correct.
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Question Description
What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. 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 What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. 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 What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. Can you explain this answer?.
What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. 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 What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. 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 What are the factors of x4+y4+x2y2?a)(x2+y2)and(x2+y2−xy)b)(x2+y2)and(x2−y2)c)(x2+y2+xy)and(x2+y2−xy)d)Factorization is not possiblCorrect answer is option 'C'. Can you explain this answer?.
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