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(2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity?
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(2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity?
Expansion of Cubes
To simplify the given expression, we can use the identity for the expansion of cubes, which states that for any real numbers a and b,
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
Given Expression
The given expression is (2x - 3y)^3 + (3y - 4z)^3 + (4z - 2x)^3.
Applying the Identity
1. For (2x - 3y)^3:
= (2x)^3 - 3(2x)^2(3y) + 3(2x)(3y)^2 - (3y)^3
= 8x^3 - 36x^2y + 54xy^2 - 27y^3
2. For (3y - 4z)^3:
= (3y)^3 - 3(3y)^2(4z) + 3(3y)(4z)^2 - (4z)^3
= 27y^3 - 108y^2z + 144yz^2 - 64z^3
3. For (4z - 2x)^3:
= (4z)^3 - 3(4z)^2(2x) + 3(4z)(2x)^2 - (2x)^3
= 64z^3 - 96z^2x + 48zx^2 - 8x^3
Final Simplified Expression
Putting it all together, the simplified expression is:
8x^3 - 36x^2y + 54xy^2 - 27y^3 + 27y^3 - 108y^2z + 144yz^2 - 64z^3 + 64z^3 - 96z^2x + 48zx^2 - 8x^3
= -36x^2y + 54xy^2 - 108y^2z + 144yz^2 - 96z^2x + 48zx^2
To simplify the given expression, we can use the identity for the expansion of cubes, which states that for any real numbers a and b,
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
Given Expression
The given expression is (2x - 3y)^3 + (3y - 4z)^3 + (4z - 2x)^3.
Applying the Identity
1. For (2x - 3y)^3:
= (2x)^3 - 3(2x)^2(3y) + 3(2x)(3y)^2 - (3y)^3
= 8x^3 - 36x^2y + 54xy^2 - 27y^3
2. For (3y - 4z)^3:
= (3y)^3 - 3(3y)^2(4z) + 3(3y)(4z)^2 - (4z)^3
= 27y^3 - 108y^2z + 144yz^2 - 64z^3
3. For (4z - 2x)^3:
= (4z)^3 - 3(4z)^2(2x) + 3(4z)(2x)^2 - (2x)^3
= 64z^3 - 96z^2x + 48zx^2 - 8x^3
Final Simplified Expression
Putting it all together, the simplified expression is:
8x^3 - 36x^2y + 54xy^2 - 27y^3 + 27y^3 - 108y^2z + 144yz^2 - 64z^3 + 64z^3 - 96z^2x + 48zx^2 - 8x^3
= -36x^2y + 54xy^2 - 108y^2z + 144yz^2 - 96z^2x + 48zx^2
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(2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity?
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(2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about (2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity?.
(2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about (2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (2x - 3y )^3 +(3y-4z)^3 +(4z-2x) ^3 simplify by using identity?.
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