Question

9 m square + 4 x square + 12 m n ​

Answer 1

Answer:

-9m2-12mn-4n2  

Final result :

 -1 • (3m + 2n)2

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((0 -  (9 • (m2))) -  12mn) -  22n2

Step  2  :

Equation at the end of step  2  :

 ((0 -  32m2) -  12mn) -  22n2

Step  3  :

Step  4  :

Pulling out like terms :

4.1     Pull out like factors :

  -9m2 - 12mn - 4n2  =   -1 • (9m2 + 12mn + 4n2)  

Trying to factor a multi variable polynomial :

4.2    Factoring    9m2 + 12mn + 4n2  

Try to factor this multi-variable trinomial using trial and error  

Found a factorization  :  (3m + 2n)•(3m + 2n)

Detecting a perfect square :

4.3    9m2  +12mn  +4n2  is a perfect square  

It factors into  (3m+2n)•(3m+2n)

which is another way of writing  (3m+2n)2

How to recognize a perfect square trinomial:  

• It has three terms  

• Two of its terms are perfect squares themselves  

• The remaining term is twice the product of the square roots of the other two terms

Step-by-step explanation:

Answer 2

$9m^{2} + 4n^{2}+ 12mn$ can also be written as; $9m^2+12mn+4n^2$

This equation is now in the form of $a^2+2ab+b^2$ which is equal to $(a+b)^2$

$(3m)^2+2$×$3m$×$2n$ + $(2n)^2$

= $(3m+2n)^2$

Regards

-PM