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    Question

    Evaluate: 297 × 303.

    A.

    89991

    B.

    89091

    C.

    90991

    D.

    79991

    Correct option is A

    Given :

    297 × 303.

    Solution:

    Notice that both numbers are close to 300, so we can use the identity for multiplying numbers close to a base:

    (ab)(a+b)=a2b2(a - b)(a + b) = a^2 - b^2​​

    Let a = 300 and b = 3. This gives: 

    297=3003and303=300+3297 = 300 - 3 \quad \text{and} \quad 303 = 300 + 3 

    Now, apply the difference of squares identity: 

    297×303=(3003)(300+3)=300232297 \times 303 = (300 - 3)(300 + 3) = 300^2 - 3^2 

    =900009=89991=90000−9=89991 

    Thus,  297 × 303 = 89991

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