Question

factorise
$( {x}^{2} - 2x) ^{2} - 2( {x}^{2} - 2x) - 3$

Answer 1

Hey!!!!

Good Afternoon

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We have

=> (x² - 2x)² - 2(x² - 2x) - 3 = 0

let (x² - 2x) = a

Then

=> a² - 2a - 3 = 0

=> a² - 3a + a - 3 = 0 (splitting method)

=> a(a - 3) + (a - 3) = 0

=> (a + 1)(a - 3) = 0

Thus x² - 2x = 3 or x² - 2x = -1

Case 1

=> x² - 2x - 3 = 0

=> (x + 1)(x - 3) = 0

=> x = -1 or x = 3

Case 2

=> x² - 2x + 1 = 0

=> x² - x - x + 1 = 0

=> x(x - 1) - (x - 1) = 0

=> (x - 1)² = 0

=> x = 1 or x = 1

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Hope this helps ✌️