Part A: The area of a square is (4a2 − 20a + 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 (9a2 − 16b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)

Part A.

Part B.

Step-by-step explanation:

Part A. In order to factor a trinomial you need to look at each number in relation to each other. In 25 and 4 are perfect squares. Furthermore, how you factor a trinomial is splitting the function up into two binomials (a function with two terms).

1. I first asked myself what two numbers multiple to get and what two numbers multiply to get a positive 25. that would be and 5. So I slowly started to form my binomials under the trinomial.

2. In my binomials I know that they both have to be negative because the third term in the trinomial is a positive 25. The second terms in the binomials multiply to form that third term. I will show you when I double check my asnwer. You use the FOIL method to check your answer. (Front, outside, inside, last)

3. Once I have both of my binomials I need to double check to see if I can form -20. The numbers that multiple to form the middle term is the front terms multiplying with the last term . This equal a -10 so we are on the right track. Two -10's will form to make -20 when you multiply the second pair of .

4. The last step is to check your answer. It's FOIL time!

Front:  (Multiply the first two front terms of each binomial)

This will equal

Outer: (Multiply the front of the first binomial with the outer of the second binomial)

This will equal

So far our equation will look like this:

Inner: (Multiply the outer of the first binomial with the front of the second binomial)

This will equal

So far our equation will look like this:

Last: (Multiply the outer of the first binomial with the outer of the second binomial)

This will equal 25

Combine and solve:

Our final equation will look like this:

We can simplify by combining the two -10's:

There you go, now we know our two binomals are correct!

Part B. In I recognize that 9 and 16 are perfect squares.

I went through the same steps in Part A for Part B.

1. I came to the formulation of these two binomials:

The reason why one binomial is positive and the second one is negative is so the middle term will cancel out and you're left with

When you multiply the Outer:

When you multiply the Inner:

So, -12 + 12 = 0 that is how they cancel.

2. You can use the FOIL method to check that these binomials are correct.

When I use the FOIL method, the two binomials check out.