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South African Mathematics Olympiad First Round

South Africa algebra

Problem

505 0^{2} - 495 0^{2} =

(A) 10 (B)

1 0^{2}

(C)

1 0^{3}

(D)

1 0^{4}

(E)

1 0^{5}

Solution

505 0^{2} - 495 0^{2} = (5050 + 4950) (5050 - 4950) = 10000 \times 100 = 1 0^{6} = 1 0^{3} .

Final answer

Techniques

Polynomial operationsIntegers