1.

Factorise :-(x² - 4x) (x² - 4x - 1) - 20​

Answer»

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LET (x^2–4x)=p

= p(p-1)-20

= p^2 -p -20

= p^2 -5p + 4P -20

= p (p-5 ) + 4 (p - 5 )

= (p - 5 ) (p + 4 )

put p = x^2 -4x

= (x^2 - 4 x - 5 ) (x ^2 -4 x + 4 )

=[ x^2–5x + x -5 ] ( x - 2 )^2

=[ x (x- 5) +1( x-5 )](x-2)^2

= (x-5) (x + 1) (x - 2 )^2

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