Question

Simplify the following using the formula: (a − b)(a + b) = a² − b²: 95 × 105

Answer 1

Here, we will use the identity  \[(a - b)(a + b) = a^2 - b^2\]

Let us consider the following product: \[95 \times 105\] 

\[\because \frac{95 + 105}{2} = \frac{200}{2} = 100\];therefore, we will write the above product as:

\[95 \times 105\]

\[ = \left( 100 + 5 \right)\left( 100 - 5 \right)\]

\[ = \left( 100 \right)^2 - \left( 5 \right)^2 \]

\[ = 10000 - 25\]

\[ = 9975\]

Thus, the answer is 9975.