Question

Using the identity for the difference of two squares, evaluate the following:

105 x 95

(a) 10000
(b) 2000
(c) 1000
(d) 9500

Answer 1

To evaluate 105 x 95 using the difference of two squares identity, rewrite it as (100 + 5)(100 - 5), which equals 100^2 - 5^2 and results in 9,975.

Step-by-step explanation:

To evaluate the product 105 x 95 using the identity for the difference of two squares. This identity states that the product of two terms (a and b) that are a specific distance apart can be represented as the squares of their average minus the square of half the distance between them. The identity is typically shown as (a + b)(a - b) = a2 - b2. For our specific problem, we can consider 105 as 'a' and 95 as 'b', and recognize that they are both 5 units away from 100.

To find 105 x 95 using the difference of two squares, we can rewrite it as:

(100 + 5)(100 - 5) = 1002 - 52 = 10,000 - 25 = 9,975.

Therefore, the product of 105 and 95 is 9,975, and the closest answer choice is (d) 9500.