Question

Simplify the following using the formula: (a − b)(a + b) = a² − b²:  9.8 × 10.2

Answer 1

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

 Let us consider the following product: \[9 . 8 \times 10 . 2\]

\[\because \frac{9 . 8 + 10 . 2}{2} = \frac{20}{2} = 10\]; therefore, we will write the above product as:

\[9 . 8 \times 10 . 2\]

\[ = \left( 10 - 0 . 2 \right)\left( 10 + 0 . 2 \right)\]

\[ = \left( 10 \right)^2 - \left( 0 . 2 \right)^2 \]

\[ = 100 - 0 . 04\]

\[ = 99 . 96\]

Thus, the answer is 99.96.