Question

Factor the expression below. 9x^2-1 A. (3x - 1)(3x - 1) B. (3x - 1)(3x + 1) C. (x - 1)(9x - 1) D. (x - 1)(9x + 1)​

Answer 1

(3x + 1) • (3x - 1)

Explanation:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

3
`{}^(2)`x
`{}^(2)` - 1

STEP

2

:

Trying to factor as a Difference of Squares:

2.1 Factoring: 9x
`{}^(2)`-1

Theory : A difference of two perfect squares, A
`{}^(2)` - B
`{}^(2)` can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A
`{}^(2)` - AB + BA - B2 =

A
`{}^(2)`- AB + AB - B2 =

A
`{}^(2)` - 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
`{}^(2)` is the square of x1

Factorization is : (3x + 1) • (3x - 1)

Final result :

(3x + 1) • (3x - 1)