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 squa
re 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.
1. If a is the length of the side of the square, then a 2 is the area of the square. The rectangle’s side lengths will be (a − 1) and (a + 1). That product, which represents the area of the rectangle, is a 2 − 1, or 1 square unit less than the area of the square.
2. Using the same logic as for Problem 1, the rectangle dimensions will be (a + 2) and (a − 2) with an area of a 2 − 4. Therefore, the area of the rectangle is 4 square units less than the area of the original square
3. It is called the product-sum method because you look for the two numbers with a product equal to the constant term of the quadratic expression and a sum equal to the coefficient of the linear term
Since there are 60 seconds in one minute, we can write this as 146,000 inches per minute. Since there are 60 * 60 = 3600 minutes in one day, we can write it as 525,600,000 inches per day. Since there are about 63360 inches in one mile, the answer is about 8295 miles per day.
