Answer:
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
