Question

The HCF of (a^2b^4 - a^2) and 4a^2b^2 + a^2b - 3a^2)

Answer 1

@perl

Answer 2

HCF = highest common factor?

Answer 3

ya

Answer 4

Compare:\[\color{red}{a^2}b^4 - \color{red}{a^2} = \color{red}{a^2}(b^4-1)\]\[4a^2b^2 + a^2b - 3a^2 = \color{red}{a^2}(4b^2+b-3)\]

Answer 5

Highest (Greatest) common factor is the variable that is common to both functions, that is the largest.

Answer 6

I would think it would be \(a^2\) since you can easily factor it out of both expressions

Answer 7

i know that a^2 is a factor but is it the highest?

Answer 8

Ah I see what you mean, then no, you can factor our the expressions involving \(b\) as well

Answer 9

If you factor both expressions you get

(a^2b^4 - a^2)
= a^2 ( b^4 - 1)
= a^2 ( b^2 + 1) (b^2 -1)
= a^2(b^2+1)(b-1)(b+1)

and
4a^2b^2 + a^2b - 3a^2)
=a^2 ( 4b^2 + b - 3 )
= a^2 ( 4b + 3) ( b + 1)

Answer 10

so what is the HCF ?

Answer 11

a^2(b+1) i see ty

Answer 12

\(4b^2+b-3 = (4b-3)(b+1)\)\[b^4-1 = (b^2+1)(b-1)(b+1)\]

Answer 13

\[4b^2+b-3 = (4b-3)\color{red}{(b+1)}\]\[b^4-1 = (b^2+1)(b-1)\color{red}{(b+1)}\]