the dimensions are: ![(2b+-+1)](/tex.php?f=(2b+-+1))
step-by-step explanation:
we want to find the dimensions of a rectangular box with volume of
![v(b)=50b^3+75b^2-2b-3](/tex.php?f=v(b)=50b^3+75b^2-2b-3)
we factor to obtain;
![v(b)=(2b+3)(25b^2-1)](/tex.php?f=v(b)=(2b+3)(25b^2-1))
we rewrite the rightmost factor to obtain;
![v(b)=(2b+)^2-1^2)](/tex.php?f=v(b)=(2b+)^2-1^2))
recall that:
![a^2-b^2=(a+b)(a-b)](/tex.php?f=a^2-b^2=(a+b)(a-b))
we apply difference of two squares formula to obtain;
![v(b)=(2b+3)(5b-1)(5b+1](/tex.php?f=v(b)=(2b+3)(5b-1)(5b+1)
hence the dimensions are
![(2b+-+1)](/tex.php?f=(2b+-+1))