Answer 1

Here, we will use the identity \[\left( x + a \right)\left( x + b \right) = x^2 + \left( a + b \right)x + ab\]

\[102 \times 106\]

\[ = \left( 100 + 2 \right)\left( 100 + 6 \right)\]

\[ = {100}^2 + \left( 2 + 6 \right)100 + 2 \times 6\]

\[ = 10000 + 800 + 12\]

\[ = 10812\]