Factorize

9(x-2y)^2 -4(x-2y)-13

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Solution

Given polynomial is 9(x − 2y)² − 4(x − 2y) − 13
Put (x − 2y) = a
∴ 9(x − 2y)² − 4(x − 2y) − 13 = 9a² − 4a − 13
= 9a² − 13a + 9a − 13
= a(9a− 13) + 1(9a − 13)
= (9a− 13)(a + 1)
= [9(x − 2y)− 13][(x − 2y) + 1]
= [9x − 18y− 13][x − 2y + 1]

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