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# factorise fully 7m - 28m^3

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factorise fully 7m - 28m^3

Guest Sep 28, 2017

#2
+1493
+2

\(7m-28m^3\)

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!

 \(4m^2-1=(2m)^2-1^2\) This is showing that it is, indeed, a difference of 2 squares. Now use the rule that \(a^2-b^2=(a+b)(a-b)\) \((2m+1)(2m-1)\)

No more progress can be made.

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

TheXSquaredFactor  Sep 28, 2017
edited by TheXSquaredFactor  Sep 28, 2017
edited by TheXSquaredFactor  Sep 28, 2017
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#1
+79786
+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)

CPhill  Sep 28, 2017
edited by CPhill  Sep 28, 2017
#2
+1493
+2

\(7m-28m^3\)

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!

 \(4m^2-1=(2m)^2-1^2\) This is showing that it is, indeed, a difference of 2 squares. Now use the rule that \(a^2-b^2=(a+b)(a-b)\) \((2m+1)(2m-1)\)

No more progress can be made.

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

TheXSquaredFactor  Sep 28, 2017
edited by TheXSquaredFactor  Sep 28, 2017
edited by TheXSquaredFactor  Sep 28, 2017
#3
+79786
+1

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

CPhill  Sep 28, 2017
#4
+5552
+1

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)

hectictar  Sep 28, 2017

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