M2 = 81 is true for ?

m = 9

m = -9

Step-by-step explanation:

1.1      Factoring:  m2-81

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 : 81 is the square of 9

Check :  m2  is the square of  m1

Factorization is :       (m + 9)  •  (m - 9)

Equation at the end of step  1  :

 (m + 9) • (m - 9)  = 0

Step  2  :

Theory - Roots of a product :

2.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

2.2      Solve  :    m+9 = 0

Subtract  9  from both sides of the equation :

                     m = -9

Solving a Single Variable Equation :

2.3      Solve  :    m-9 = 0

Add  9  to both sides of the equation :

                     m = 9