Part A: The area of a square is (9x2 + 24x + 16) 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 (16x2 − 25y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

(10 points)

Part A: Since it represents the area of a square, we expect

to be a perfect square. In general, a perfect square has the following form:

If you match your expression with the generic form, you'll see that:

Since is the square of and 16 is the square of 4, those would be your and values. In order to decide if your side is or , just look at the sign of the middle term and you're done!

Part B: in this case, you'll need the formula

Apply this formula to your values and you'll get the dimensions of the rectangle ( and are squares of who...?)

since the airplane is moving with constant speed then the distance travelled can be calculated by x=u*t

in km/h would be:

x=640*3.5=2.240 km

in m/s would be:

u=640 km/h= 640.000 m/h =640.000/ 3600 m/s =177.8 m/s

t= 3.5 h= 3.5 * 3600 s=12.600 s

then x=u*t= 177.8*12.600= 2.240.280 m