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(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it?
Verified Answer
(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simpli...
Here a^2-b^2+b^2-c^2+c^2-a^2=0
If a + b + c = 0 then a^3 + b^3 + c^3 = 3abc
so
(a^2 - b^2)^3 +(b2-c2)^3 + (c^2-a^2) = 3(a^2-b^2)(b^2-c^2)(c^2-a^2)
This question is part of UPSC exam. View all Class 9 courses
Most Upvoted Answer
(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simpli...
Just put the formula i.e a^3+b^3+c^3=3abc. in both numerator and denominator.
Community Answer
(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simpli...
Start by expanding the given expression:
- Start by expanding the terms inside the brackets using the formula for the difference of squares.
- (a^2 - b^2)^3 = (a - b)(a^2 + ab + b^2)
- (b^2 - c^2)^3 = (b - c)(b^2 + bc + c^2)
- (c^2 - a^2)^3 = (c - a)(c^2 + ac + a^2)
Combine like terms:
- Expand the terms further to simplify the expression.
- (a - b)(a^2 + ab + b^2) + (b - c)(b^2 + bc + c^2) + (c - a)(c^2 + ac + a^2)
- Simplify the expression by combining like terms.
Apply the formula for a^3 + b^3 + c^3 - 3abc:
- Use the formula (a^3 + b^3 + c^3 - 3abc) to further simplify the expression.
- Factor out common terms and simplify the expression to get the final result.
Final simplified expression:
- The final expression should be simplified to a more manageable form after applying the formula and combining like terms.
- This will give you the simplified version of the given expression.
- Start by expanding the terms inside the brackets using the formula for the difference of squares.
- (a^2 - b^2)^3 = (a - b)(a^2 + ab + b^2)
- (b^2 - c^2)^3 = (b - c)(b^2 + bc + c^2)
- (c^2 - a^2)^3 = (c - a)(c^2 + ac + a^2)
Combine like terms:
- Expand the terms further to simplify the expression.
- (a - b)(a^2 + ab + b^2) + (b - c)(b^2 + bc + c^2) + (c - a)(c^2 + ac + a^2)
- Simplify the expression by combining like terms.
Apply the formula for a^3 + b^3 + c^3 - 3abc:
- Use the formula (a^3 + b^3 + c^3 - 3abc) to further simplify the expression.
- Factor out common terms and simplify the expression to get the final result.
Final simplified expression:
- The final expression should be simplified to a more manageable form after applying the formula and combining like terms.
- This will give you the simplified version of the given expression.
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(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it?
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(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about (a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it?.
(a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about (a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (a^2-b^2)^3 +(b^2-c^2)^3 +(c^2-a^2)^3/(a+b)^3 +(b-c)^3 +(c-a)^3 simplify it?.
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