Worth 20 pts. and ! part a: the area of a square is (4x2 + 20x + 25) square units. determine the length of each side of the square by factoring the area expression completely. show your work. (5 points) part b: the area of a rectangle is (4x2 − 9y2) square units. determine the dimensions of the rectangle by factoring the area expression completely. show your work. (5 points)

step-1 : multiply the coefficient of the first term by the constant      4  •  25  =  100  step-2 : find two factors of    100    whose sum equals the coefficient of the middle term, which is     20  .

10+10=20

step-3 : rewrite the polynomial splitting the middle term using the two factors found in step  2  above,    10    and    10                                            4x2  + 10x  +  10x + 25step-4 : add up the first 2 terms, pulling out like factors  :                                         2x  •  (2x+5)                          add up the last 2 terms, pulling out common factors  :                                         5  •  (2x+5)step-5  :   add up the four terms of step  4  :                                         (2x+5)^2

part b:

step-1

(4 • (x2)) - 32y2 = 0

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