Factor the expression below 81a²-25

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)

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.