Find the HCF and LCM of:

Question

1 + 4x + 4x^2 - 16x^4.. ,1 + 2x - 8x^3 - 16x^4.., 16x^4 + 4x^2 + 1

Answer 1

1 + 4x + 4x^2 - 16x^4.. ,1 + 2x - 8x^3 - 16x^4.., 16x^4 + 4x^2 + 1

is there a significance to the .. at the end of the first term?

if not, then

1 + 4x + 4x^2 - 16x^4
= (1+4x) + 4x^2(1 - 4x^2)
= (1 + 4x) + 4x^2(1 - 2x)(1 + 2x)

1 + 2x - 8x^3 - 16x^4
= (1+2x) - 8x^3(1 + 2x^2)

16x^4 + 4x^2 + 1
= (16x^4 + 8x^2 + 1) - 4x^2
= (4x^2 + 1)^2 - 4x^2
= (4x^2 + 1 + 2x)(4x^2 + 1 - 2x)
= (4x^2+2x+1)(4x^2-2x+1)

At the moment I can't see anything else to do with the first two.

Answer 2

2x^2(x^-a^2);3x^3(x^3-a^3) find lcm

Answer 3

in 2nd exp after taking -8x^3 common there should only be (1+2x)

Answer 4

Find the HCF and LCM of:
1 + 4x + 4x^2 - 16x^4.. ,1 + 2x - 8x^3 - 16x^4..,

Answer 5

First exp=1+4x+4x^2-16x^4
=(1)^2+2.1.2x+(2x)^2-16x^4
=(1+2x)^2-(4x^2)^2
=(1+2x+4x^2) (1+2x-4x^2)
Second exp.=1+2x-8x^3-16x^4
=(1)^3-(2x)^3+2x-16x^4
=(1-2x)(1+2x+4x^2)+2x(1-8x^3)
=(1+2x)(1-2x)(1+2x+4x^2)

:HCF=(1+2x+4x^2)

Answer 6

1+2x+4x^2

Answer 7

The HCF of the first two expressions is indeed:

$1 + 4x + 4x^2 - 16x^4 = (1 + 2x)(1 - 2x + 4x^2)$

$1 + 2x - 8x^3 - 16x^4 = (1 + 2x)(1 - 2x + 4x^2) - 8x^3$

Therefore, the HCF is $1 - 2x + 4x^2$.