Question

How do you factor `7h^4-7p^4`?

Answer 1

`7(h^2+p^2)(h+p)(h-p)`

Explanation:

When factorising :

1) Firstly, look for common factors

2) Secondly look for difference of squares

In this case

`7h^4-7p^4`

by inspection we see `7` is a common factor, so:

`=7(h^4-p^4)`

now look for difference of squares

`ie" "a^2-b^2=(a+b)(a-b)`

if both powers are even then we have DoS

`7(h^4-p^4)=7(h^2+p^2)(h^2-p^2)`

now look and see if we can factorise anything further.

the first bracket can not be factorised using real numbers, but the second bracket is DoS again.

so we have

`7(h^2+p^2)(h+p)(h-p)`

and that is now fully factorised.

***If you allow complex numbers then the first bracket can be factorised using DoS

`=7(h+ip)(h-ip)(h+p)(h-p)`