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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