If the dimensions were all the same number ... the box was a cube ...
then each dimension would be (the cube root of 13,800) cm.
∛13,800 = 23.986... (rounded)
so the place to look is around 23 .
(22 x 23 x 24) = 12,144 <== too small; go up one integer
(23 x 24 x 25) = 13,800 <== Eureka !
The consecutive integers are 23, 24, and 25 .
Factor 25 out of 25a^2−100.
Factor 25 out of 25a^2.
25(a^2)−100
Factor 25 out of −100.
25a^2+25⋅−4
Factor 25 out of 25a^2+25⋅−4.
25(a^2−4)
Rewrite 4 as 2^2.
25(a^2−2^2)
Factor.
Since both terms are perfect squares, factor using the difference of squares formula, a^2−b^2=(a+b)(a−b) where a=a and b=2.
25((a+2)(a−2))
Remove unnecessary parentheses.
25(a+2)(a−2)
I believe this is correct.
If you join the arrays so that they fit as a rectangle, you get 5x6.