Question

desconponer m2-m3+1-m

Answer 1

Respuesta:(-m - 1) • (1 - m)2

Explicación paso a paso:

Step by Step Solution

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Reformatting the input :

Changes made to your input should not affect the solution:

(1): "m3"   was replaced by   "m^3".  1 more similar replacement(s).

STEP

1

:

Checking for a perfect cube

1.1    -m3+m2+m-1  is not a perfect cube

Trying to factor by pulling out :

1.2      Factoring:  -m3+m2+m-1

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  m-1

Group 2:  -m3+m2

Pull out from each group separately :

Group 1:   (m-1) • (1)

Group 2:   (m-1) • (-m2)

              -------------------

Add up the two groups :

              (m-1)  •  (1-m2)

Which is the desired factorization

Trying to factor as a Difference of Squares:

1.3      Factoring:  1-m2

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  1  is the square of  1

Check :  m2  is the square of  m1

Factorization is :       (1 + m)  •  (1 - m)

1.4    Rewrite  (m-1)  as (-1) •  (1-m)

Multiplying Exponential Expressions:

1.5    Multiply  (1-m)  by  (1-m)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is  (1-m)  and the exponents are :

         1 , as  (1-m)  is the same number as  (1-m)1

and   1 , as  (1-m)  is the same number as  (1-m)1

The product is therefore,  (1-m)(1+1) = (1-m)2

Final result :

 (-m - 1) • (1 - m)2