#2**+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

#1**+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

#2**+2 **

Best Answer

\(7m-28m^3\)

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