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