Amazing 2 9 9 X 9

1. 3x 9 X 2 9
2. Amazing 2 9 9 X 9 9
3. Amazing 2 9 9 X 9
4. Amazing 2 9 9 X 9 9 Worsted Wool Rugs
5. Amazing 2 9 9 X 9 11 Bedrooms

Reformatting the input :

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Changes made to your input should not affect the solution:
(1): 'x2' was replaced by 'x^2'. 1 more similar replacement(s).

Step 1 :

3x 9 X 2 9

Amazing 2 9 9 X 9 9

Equation at the end of step 1 :

Equation at the end of step 2 :

Step 3 :

Checking for a perfect cube :

3.1 9x³+9x²-x-1 is not a perfect cube

Amazing 2 9 9 X 9

Trying to factor by pulling out :

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3.2 Factoring: 9x³+9x²-x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -x-1
Group 2: 9x³+9x²
Pull out from each group separately :
Group 1: (x+1) • (-1)
Group 2: (x+1) • (9x²)
-------------------
Add up the two groups :
(x+1) • (9x²-1)
Which is the desired factorization

Trying to factor as a Difference of Squares :

3.3 Factoring: 9x²-1
Theory : A difference of two perfect squares, A² - B²can 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 : 1 is the square of 1
Check : x²is the square of x¹
Factorization is : (3x + 1) • (3x - 1)
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Final result :

Reformatting the input :

Changes made to your input should not affect the solution:
(1): 'x2' was replaced by 'x^2'. 1 more similar replacement(s).

Amazing 2 9 9 X 9 9 Worsted Wool Rugs

Step 1 :

Amazing 2 9 9 X 9 11 Bedrooms

Equation at the end of step 1 :

Equation at the end of step 2 :

Step 3 :

Checking for a perfect cube :

3.1 9x³+9x²-x-1 is not a perfect cube
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Trying to factor by pulling out :

3.2 Factoring: 9x³+9x²-x-1
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -x-1
Group 2: 9x³+9x²
Pull out from each group separately :
Group 1: (x+1) • (-1)
Group 2: (x+1) • (9x²)
-------------------
Add up the two groups :
(x+1) • (9x²-1)
Which is the desired factorization

Trying to factor as a Difference of Squares :

3.3 Factoring: 9x²-1
Theory : A difference of two perfect squares, A² - B²can 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 : 1 is the square of 1
Check : x²is the square of x¹
Factorization is : (3x + 1) • (3x - 1)

Final result :