Part a.) the area of a square is (16x^2-8x+1) square units. determine the length of each side of the square by factoring the areas expressions completely. show all work
part b.) the area of a rectangle is (81x^2-4y^2)square units. determine the dimensions of the rectangle by factoring the area of the expression. show all work
part c.) the volume of a rectangular box is (x^3-9x^2-4x+36) cubic units. determine the dimensions of the rectangular box by factoring the volume expression completely. show all work

Answers are
a) the area of a square is A = L^2= 16x^2 - 8x+1= (4x  -1)^2, so                    sqrt (L^2)= sqrt (4x  -1)^2, and so L = 4x - 1,  
b) the area of a rectangle is A = h x w = 81x^2-4y^2 = (9x- 2y) (9x + 2y)
so w =  (9x- 2y)  and h=(9x + 2y)
c) let be f(x) = x^3-9x^2-4x+36, so f(2) = 8-36-8+36=0, f(x) can be written as 
f(x) = (x - 2) (ax^2 + bx +c), we must find a, b and c
(ax^2 + bx +c)=x^3-9x^2-4x+36  / x - 2, after the division we have
ax^2 + bx +c = x^2-7x-18, and x= - 2 is a zero of x^2-7x-18, so x^2-7x-18 = (x +2) (ax + b), ax + b =x^2-7x-18  / x + 2 = x - 9

finally V = h x w x L =(x - 2)  (x +2) (x - 9), 

Aand b are correctly balanced reactions. they have the same number of atoms in both sides of the reaction