Step 1 :
Equation at the end of step 1 :
108 - 3x2
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
108 - 3x2 = -3 • (x2 - 36)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 36
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 : x2 is the square of x1
Factorization is : (x + 6) • (x - 6)
Final result :
-3 • (x + 6) • (x - 6)
