Question

Factorise completely 9a^2-1

Answer 1

Answer:

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

Step-by-step 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

ANSWER

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

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:

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