1. Use algebra to explain how you know that a rectangle with side lengths one less and one more than a square will always be 1 square unit smaller than the square. 2. What is the difference in the areas of a square and rectangle if the rectangle has side lengths 2 less and 2 more than a square? Use algebra or a geometric model to compare the areas and justify your answer. 3. Explain why the method for factoring shown in this lesson is called the product-sum method.

Okay so n is going to represent our first number. since the second number of five times greater than n, the second number will be represented as 5n. for us to figure out the two  numbers we need to have  the value of n first. this is going to be done by adding the two numbers together, n and 5n. it can be simplified as 6n, which the problem states is equal to 72. divide 72 by 6n and you can solve for n.  n+5n=726n=72n=(72/6)n=12  now that we know the value of n, we have to multiply 5 times 12 which equals 60. so our two numbers/integers are 12 and 60