factorise fully 7m - 28m^3

\(7m-28m^3\)

The first step is to figure out the GCF. Of course, Cphill has already figured it out and has provided an explanation that it is 7. However, you can also divide by -7, which is what I will do here.

\(-7m(-1+4m^2)=-7m(4m^2-1)\)

4m^2-1 happens to be a difference of 2 squares, though! We must factorize that! 

No more progress can be made.

Therefore, the final factorization is \(-7m(2m+1)(2m-1)\)

7m - 28m^3           

The greatest common factor   between   7 and  28   = 7

The greatest common factor between m and m^3 =   m

So.... the greatest common factor  ( GCF )  = 7m

So we will have

7m ( a  -  b)

To  find out  what  " a '  will be....divide the first term of the given expression , 7m,  by the GCF

So      7m  /   7m    = 1

To find out what  "b" will be......divide the second term of the given expression, 28m^3,  by the GCF

So       28m^3  / 7m  =      4m^2

So......the complete factorization is

7m  ( 1  - 4m^2)

Thanks, X^2....I neglected to spot that 1 - 4m^2  could be factored further as  (1 -2m) (1 + 2m)  !!!!!

I just noticed something that is kind of interesting!!

You could also have factored it as    (7m)(1 + 2m)(1 – 2m)

So...        ( – 7m)(2m + 1)(2m – 1)  =  (7m)(1 + 2m)(1 - 2m)

which means....                 – (a + b)(a – b)  =  (b + a)(b – a)