Question

add 4m n^2 , 8m n^2 , 12m n^ 2 ​

Answer 1

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

((((4•(m2))•n)+(22•3m2))-8mn)-24m

STEP

2

:

Equation at the end of step

2

:

(((22m2 • n) + (22•3m2)) - 8mn) - 24m

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

4m2n + 12m2 - 8mn - 24m =

4m • (mn + 3m - 2n - 6)

Trying to factor a multi variable polynomial :

4.2 Split mn + 3m - 2n - 6

into two 2-term polynomials

+ 3m + mn and - 2n - 6

This partition did not result in a factorization. We'll try another one:

mn + 3m and - 2n - 6

This partition looks good

4.3 Pull out from each binomial separately

mn + 3m = m • (n + 3)

- 2n - 6 = - 2 • (n + 3)

4.4 Add up to arrive at the desired factorization

mn + 3m - 2n - 6 = (m - 2) • (n + 3)

Final result :

4m • (m - 2) • (n + 3)

Answer 2

Answer:

4m • (m - 2) • (n + 3)

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 ((((4•(m2))•n)+(22•3m2))-8mn)-24m

STEP

2

:

Equation at the end of step

2

:

 (((22m2 • n) +  (22•3m2)) -  8mn) -  24m

STEP

3

:

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  4m2n + 12m2 - 8mn - 24m  =

 4m • (mn + 3m - 2n - 6)

Trying to factor a multi variable polynomial :

4.2       Split       mn + 3m - 2n - 6

            into two 2-term polynomials

             + 3m + mn   and     - 2n - 6

            This partition did not result in a factorization. We'll try another one:

            mn + 3m   and     - 2n - 6

            This partition looks good

4.3       Pull out from each binomial separately

            mn + 3m   =   m • (n + 3)

             - 2n - 6   =    - 2 • (n + 3)

4.4       Add up to arrive at the desired factorization

            mn + 3m - 2n - 6  =  (m - 2) • (n + 3)

Final result :

 4m • (m - 2) • (n + 3)