Question

Factorise: (x ^ 2 - 4x)(x ^ 2 - 4x - 1) - 2​

Answer 1

(x

2

−4x)(x

2

−4x−1)−20

let (x²−4x)=P

P(P−1)−20

P²−P−20

P²−5P+4P−20

P(P−5)+4(P−5)

(P+4)(P−5)

put P=x

2

−4x

(x²−4x+4)(x²−4x−5)

(x−2)

2

(x+1)(x−5)

Answer 2

Answer:

$(x^{2}-4x-2)(x^{2}-4x+1)$

Step-by-step explanation:

  $(x^{2}-4x)(x^{2}-4x-1)-2$

= $a(a-1)-2$                                     [let $x^{2} - 4x=a$]

= $a^{2} - a - 2$

= $a^{2} -2a + a -2$

= $a(a-2)+1(a-2)$

= $(a-2)(a+1)$

= $(x^{2}-4x-2)(x^{2}-4x+1)$             [As $a=x^{2}-4x$]

Ans:-  $(x^{2}-4x-2)(x^{2}-4x+1)$