Question

64x^4+48x^2+9 factorise using (a+b)^2 or (a-b)^2​

Answer 1

You (try to) divide your number by successive primes

2,3,5,7,11..

Example :

Say you want to factor

756

Even number, divide by 2:

756=2⋅378

Even, divide by 2:

756=2⋅2⋅189

Odd, so try 3:

756=2⋅2⋅3⋅63

And again:

756=2⋅2⋅3⋅3⋅21

And again:

756=2⋅2⋅3⋅3⋅3⋅7

7 is a prime, so you're finished.

You write the result as

756=22⋅33⋅7

Remark :

You never have to try a prime that is larger than the square root of the number left, because if that would divide evenly, the result is a smaller number, and you would have already tried that.