Answer:
(3x + 1) • (3x - 1)
Step-by-step explanation:
Step by Step Solution
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STEP
1
:
Equation at the end of step 1
3[tex]{}^{2}[/tex]x[tex]{}^{2}[/tex] - 1
STEP
2
:
Trying to factor as a Difference of Squares:
2.1 Factoring: 9x[tex]{}^{2}[/tex]-1
Theory : A difference of two perfect squares, A[tex]{}^{2}[/tex] - B[tex]{}^{2}[/tex] can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A[tex]{}^{2}[/tex] - AB + BA - B2 =
A[tex]{}^{2} [/tex]- AB + AB - B2 =
A[tex]{}^{2}[/tex] - 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 : x[tex]{}^{2}[/tex] is the square of x1
Factorization is : (3x + 1) • (3x - 1)
Final result :
(3x + 1) • (3x - 1)
