Answer:3x • (2x2 - 3)
Explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2". 3 more similar replacement(s).
STEP
1
:
Equation at the end of step 1
((3•(x3))+(4•(x2)))+(((3•(x3))-22x2)-9x)
STEP
2
:
Equation at the end of step
2
:
((3•(x3))+(4•(x2)))+((3x3-22x2)-9x)
STEP
3
:
Equation at the end of step
3
:
((3 • (x3)) + 22x2) + (3x3 - 4x2 - 9x)
STEP
4
:
Equation at the end of step
4
:
(3x3 + 22x2) + (3x3 - 4x2 - 9x)
STEP
5
:
STEP
6
:
Pulling out like terms
6.1 Pull out like factors :
6x3 - 9x = 3x • (2x2 - 3)
Trying to factor as a Difference of Squares:
6.2 Factoring: 2x2 - 3
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 : 2 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Final result :
3x • (2x2 - 3)