Factor the expression 9x^2-1

(3x - 1) (3x + 1)

Step-by-step explanation:

9x² - 1 ← is a difference of squares and factors in general as

a² - b² = (a - b) (a + b)

9x² - 1

= (3x) ² - 1² ← with a = 3x and b = 1, thus

= (3x - 1) (3x + 1)

Since both terms are perfect squares, factor using the difference of squares formula,

a

2

-

b

2

=

(

a

+

b

)

(

a

-

b

)

where

a

=

3

x

and

b

=

1

.

(

3

x

+

1

)

(

3

x

-

1

)