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Question

12(x​​​​​​2​​​+7)2-8(x​​​​​​2​​​​​+7)2(2x-1)-15(2x-1)2

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Solution

Let a = x^2 + 7x and b = 2x - 1
=> 12(x² + 7x)² - 8 (x² +7x )(2x -1) - 15 (2x - 1)²
= 12a^2 - 8ab - 15b^2
= 12a^2 - 18ab + 10ab - 15b^2
= 6a (2a - 3b) + 5b (2a - 3b)
= (2a - 3b) (6a + 5b)
Plugging the values of a and b,
= [2(x^2 + 7x) - 3(2x - 1)] *[6(x^2 + 7x) + 5(2x - 1)]
= (2x^2 + 8x + 3) (6x^2 + 52x - 5)

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