Answer: The dimensions are,
(5b+1) × (5b-1) × (2b+3)
Step-by-step explanation:
Here, the given volume of the box,
[tex]V=50b^3 + 75b^2 - 2b - 3[/tex]
[tex]=25b^2(2b+3)-2b-3[/tex]
[tex]=25b^2(2b+3)-1(2b+3)[/tex]
[tex]=(25b^2-1)(2b+3)[/tex]
[tex]=((5b)^2-(1)^2)(2b+3)[/tex]
[tex]=(5b+1)(5b-1)(2b+3)[/tex] ( a² - b² = (a+b)(a-b) )
[tex]\implies V=(5b+1)\times (5b-1)\times (2b+3)[/tex].
Since, the volume of a rectangular box is,
V = l × w × h
Where l, w and h are the dimensions of the box.
By comparing,
The dimensions of the box are (5b+1) × (5b-1) × (2b+3)
