Factoring 4 terms with a difference of squares as two of the 4 terms

Question

Can someone help show me step by step how to factor:

$9x^2 - 24xy + 16y^2 - 81$

I see a difference of squares in the last two terms and am stuck at this stage (did I start wrong in doing the factoring?) :

$9x^2 - 24xy + (4y+9)(4y-9)$

Please show me the steps to get the final factored form to:

$(3x-4y+9)(3x-4y-9)$

Answer 1

HINT: $$9x^2 - 24xy + 16y^2=(3x-4y)^2$$

Answer 2

HINT: $$(a-9)(a+9)$$ is the main indea