[tex]\displaystyle\bf\\\text{\bf We use the formula: }~~~~a^2-b^2=(a-b)(a+b)\\\\81a^2-25=9^2a^2-5^2=(9a)^2-5^2=\boxed{\bf(9a-5)(9a+5)}[/tex]
81a² - 25
[ax² + bx + c] Multiply the first and last term (a and c)
81 × 25 = 2025
Find the factors of 2025 that cancel each other out. [This is because you don't have "bx", and you are trying to find the middle term]
So √2025 = 45 45 multiplied by 45 equals 2025, and they cancel out
Now you can do:
81a² - 45a + 45a - 25 Factor 9a from (81a² - 45a), and factor 5 from (45a - 25)
9a(9a - 5) + 5(9a - 5) Factor out (9a - 5)
(9a - 5)(9a + 5)
