Question

Using the identity, evaluate the following:
(105 × 95)

Answer 1

To evaluate (105 × 95), we can use the difference of squares formula, treating 105 as 'a + b' and 95 as 'a - b'. The final product of 105 and 95 is 9975.

Step-by-step explanation:

To evaluate the expression (105 × 95) using a mathematical identity, we can use the difference of squares formula, which is a² - b² = (a + b)(a - b). Here, we can consider 105 as 'a + b' and 95 as 'a - b', which means 'a' would be 100 and 'b' would be 5 in our case because 100 + 5 = 105 and 100 - 5 = 95.

Applying the difference of squares:

• a² - b² = (100² - 5²)
• 10000 - 25 = 9975

Therefore, the product of 105 and 95 is 9975. This is a simple and quick way to multiply numbers that are equidistant from a common base, in this case, the base being 100.