Part a: the area of a square is (9x2 − 18x + 9) square units. determine the length of each side of the square by factoring the area expression completely. show your work. part b: the area of a rectangle is (25x2 − 4y2) square units. determine the dimensions of the rectangle by factoring the area expression completely. show your work.

A) 9x^2 -18x +9 = 9(x^2 -2x +1) = 3^2*(x -1)^2 = (3(x -1))^2

The length of each side is 3(x -1).

B) 25x^2 -4y^2 = (5x)^2 -(2y)^2 = (5x -2y)*(5x +2y)

The dimensions are (5x -2y) and (5x +2y).


The first question makes use of the "square of a binomial" special form:
  (a -b)^2 = a^2 -2ab +b^2

The second question makes use of the "difference of squares" special form:
  a^2 -b^2 = (a -b)(a +b)