Question

Simplify the following using the formula: (a − b)(a + b) = a² − b²: 113 × 87

Answer 1

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

Let us consider the following product: \[113 \times 87\]

\[\because \frac{113 + 87}{2} = \frac{200}{2} = 100\] therefore, we will write the above product as:

\[113 \times 87\]

\[ = \left( 100 + 13 \right)\left( 100 - 13 \right)\]

\[ = \left( 100 \right)^2 - \left( 13 \right)^2 \]

\[ = 10000 - 169\]

\[ = 9831\]

Thus, the answer is 9831.