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Evaluate 297×303.
89991
89091
90991
79991
89991
Express the numbers as (300−3) and (300+3) and use the algebraic identity (a−b)(a+b)=a2−b2 to calculate mentally in seconds.
Expression to evaluate: 297 x 303
(a−b)(a+b)=a2−b2
Express the numbers as (300−3) and (300+3) and use the algebraic identity (a−b)(a+b)=a2−b2 to calculate mentally in seconds.
Multiplying directly digit by digit leading to calculation errors under time pressure.
Rewrite the numbers using a common base
Express 297 as (300−3) and 303 as (300+3).
297×303=(300−3)(300+3)
Apply algebraic identity
Use the standard difference of squares identity: (a−b)(a+b)=a2−b2, where a=300 and b=3.
(300−3)(300+3)=3002−32
Calculate the squares
Compute 3002=90000 and 32=9.
90000−9=89991
A is correct because the product calculated using the algebraic identity is 89991.
Recognizing base numbers like 100, 1000, or 50 helps simplify multiplication and squaring problems across quantitative aptitude exams.
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