Question

Factorise 9a² - 9b² + 6a + 1

Answer 1

$9a^2 +6a+1-9b^2 = (3a+1)^2-(3b)^2 = (3a+1+3b)(3a+1-3b)$

Answer 2

Given that 
$9a^2 - 9b^2 + 6a + 1$

Rewriting the given expression,
$9a^2 + 6a + 1- 9b^2$

$(3a + 1)^2 - (3b)^2$    {using the formula $a^2 + b^2 +2ab = (a+b)^2$}

$(3a + 1+3b)(3a + 1-3b)$   {Using the formula $a^2 - b^2 = (a+b)(a-b)$}