(A) We can write the expression as:$101 \times 102 = (100 + 1)(100 + 2)$Using the algebraic identity $(x + a)(x + b) = x^2 + (a + b)x + ab$,where $x =

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(A) We can write the expression as:$101 \times 102 = (100 + 1)(100 + 2)$Using the algebraic identity $(x + a)(x + b) = x^2 + (a + b)x + ab$,where $x = 100$,$a = 1$,and $b = 2$:$(100 + 1)(100 + 2) = (100)^2 + (1 + 2)(100) + (1)(2)$$= 10000 + (3)(100) + 2$$= 10000 + 300 + 2$$= 10302$