Question

Factorise (1 – 2x – x2) (1 – 2x + 3x2) + 4x4

Answer 1

Step-by-step explanation:

=(1-2x-2x)×(1-2x)+16

=(1-4) ×(7-2x)+16

=7-2x-28x+8x^2+12

=23-30x+8x^2

=8x^2-30x+23

Answer 2

Answer:

(x-1)⁴

Step-by-step explanation:

We have to factorize the expression,

(1-2x-x²)(1-2x+3x²)+4x⁴

First simplify the above expression. We get,

=1-2x+3x²-2x+4x²-6x³-x²+2x³-3x⁴+4x⁴

=x⁴-4x³+6x²-4x+1

Here we have to use the vanishing method. If x=1 then the above expression becomes zero. Hence, (x-1) will be a factor of the above expression.

Then arrange the expression so as to get (x-1) as common.

=x⁴-x³-3x³+3x²+3x²-3x-x+1

=x³(x-1)-3x²(x-1)+3x(x-1)-1(x-1)

=(x-1)(x³-3x²+3x-1)

=(x-1)(x-1)³

=(x-1)⁴

Hence this is the required factorization.

So, the factors are (x-1), (x-1)², (x-1)³, (x-1)⁴. (Answer)