Question

Factorise completely 9a^2-1

Answer 1

(3a-1)(3a+1)

Explanation:

We can quickly see with this problem that it is the difference of two squares as 9a^2 is (3a)^2 and 1 is 1^2 and therefore can factorise quickly using this rule.

x^2-y^2 = (x-y)(x+y) where x = 3a and y = 1

Answer 2

`{(3 {a})^(2) } - {1}^(2) = (3a + 1)(3a - 1)`

EXPLANATION

We want to simplify completely:

`9 {a}^(2) - 1`

We express the two terms as difference of two squares;

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

Recall and apply the following identity;

`{x}^(2) - {y}^(2) = (x + y)(x - y)`

We apply this identity to obtain:

`{(3 {a})^(2) } - {1}^(2) = (3a + 1)(3a - 1)`