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Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³?
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Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³?
Factorising the given expression:
The given expression is: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³.
Step 1: Rewrite the expression
Rewrite the expression using the factored form of a³ + b³ + c³ which is (a + b + c)(a² + b² + c² - ab - bc - ac).
Step 2: Factorise each term
Factorise each term separately to apply the formula.
Step 3: Apply the formula
Apply the factored form of a³ + b³ + c³ to factorise the given expression.
Final answer:
After applying the formula and simplifying, the factored form of the given expression is (2x + 5y - 5/3y + 3/4z - 3/4z - 2/3x)(4x² + 25y² + 25/9y² + 9/16z² + 9/16z² + 4/9x² - 20xy + 10xz - 15yz).
The given expression is: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³.
Step 1: Rewrite the expression
Rewrite the expression using the factored form of a³ + b³ + c³ which is (a + b + c)(a² + b² + c² - ab - bc - ac).
Step 2: Factorise each term
Factorise each term separately to apply the formula.
Step 3: Apply the formula
Apply the factored form of a³ + b³ + c³ to factorise the given expression.
Final answer:
After applying the formula and simplifying, the factored form of the given expression is (2x + 5y - 5/3y + 3/4z - 3/4z - 2/3x)(4x² + 25y² + 25/9y² + 9/16z² + 9/16z² + 4/9x² - 20xy + 10xz - 15yz).
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Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³?
Question Description
Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³?.
Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Factorise: 1/27(2x + 5y)³ + (-5/3y + 3/4z)³ - (3/4z + 2/3x)³?.
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