Question

Simplify the following using the formula: (a − b)(a + b) = a² − b²: 1.8 × 2.2

Answer 1

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

Let us consider the following product: \[1 . 8 \times 2 . 2\] 

\[\because \frac{1 . 8 + 2 . 2}{2} = \frac{4}{2} = 2\]; therefore, we will write the above product as:

\[1 . 8 \times 2 . 2\]

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

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

\[ = 4 - 0 . 04\]

\[ = 3 . 96\]

Thus, the answer is 3.96.