Answer:
(x + 3) • (x - 3) • (x + 6)
Step-by-step explanation:
Step 1 :
Equation at the end of step 1 :
(((x3) + (2•3x2)) - 9x) - 54
Step 2 :
Checking for a perfect cube :
2.1 x3+6x2-9x-54 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3+6x2-9x-54
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -9x-54
Group 2: 6x2+x3
Pull out from each group separately :
Group 1: (x+6) • (-9)
Group 2: (x+6) • (x2)
-------------------
Add up the two groups :
(x+6) • (x2-9)
Which is the desired factorization
Trying to factor as a Difference of Squares :
2.3 Factoring: x2-9
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 : 9 is the square of 3
Check : x2 is the square of x1
Factorization is : (x + 3) • (x - 3)
Final result :
(x + 3) • (x - 3) • (x + 6)
Processing ends successfully
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