Answer: Two solutions were found :
q = 6
q = -6
Step-by-step explanation: Factoring: 36-q2
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 : 36 is the square of 6
Check : q2 is the square of q1
Factorization is : (6 + q) • (6 - q)
(q + 6) • (6 - q) = 0
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.
Solve : q+6 = 0
Subtract 6 from both sides of the equation :
q = -6
Solve : -q+6 = 0
Subtract 6 from both sides of the equation :
-q = -6
Multiply both sides of the equation by (-1) : q = 6
