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(6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value of 1/13 * (B ^ 2 - A ^ 2) = ?
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(6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value ...


Given Expression:
(6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2)

Expanding the Cubes:
(216x^3 + 3 * 216x^2 * 5y + 3 * 216x * 25y^2 + 125y^3) + (216x^3 - 3 * 216x^2 * 5y + 3 * 216x * 25y^2 - 125y^3) = 36(A * x^3 + Bx * y^2)

Combining Like Terms:
432x^3 + 2700x^2y + 2700xy^2 + 1250y^3 + 432x^3 - 2700x^2y + 2700xy^2 - 1250y^3 = 36(A * x^3 + Bx * y^2)

Simplifying:
864x^3 + 5400xy^2 = 36(A * x^3 + Bx * y^2)

Comparing Coefficients:
864 = 36A
A = 24

5400 = 36B
B = 150

Calculating 1/13 * (B^2 - A^2):
1/13 * (150^2 - 24^2)
1/13 * (22500 - 576)
1/13 * 21924
1686

Therefore, the value of 1/13 * (B^2 - A^2) is 1686.
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(6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value of 1/13 * (B ^ 2 - A ^ 2) = ?
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(6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value of 1/13 * (B ^ 2 - A ^ 2) = ? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about (6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value of 1/13 * (B ^ 2 - A ^ 2) = ? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for (6x + 5y) ^ 3 + (6x - 5y) ^ 3 = 36(A * x ^ 3 + Bx * y ^ 2) then value of 1/13 * (B ^ 2 - A ^ 2) = ?.
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