Question

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.

Answer 1

Explanation:

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