Factorise :

$(x^{2} - 3 x) (x^{2} - 3 x - 1) - 20$

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Solution

(x²- 3x)(x²- 3x - 1) - 20

= (x² - 3x)[(x² - 3x) - 1] - 20

= a[a - 1] - 20 ….(Taking x² - 3x = a)

= a² - a - 20

= a² - 5a + 4a - 20

= a(a - 5) + 4(a - 5)

= (a - 5)(a + 4)

= (x² - 3x - 5)(x² - 3x + 4)

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