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The square of 42 is:
1504
1564
1764
1664
1764
Use the algebraic expansion identity 422=(40+2)2=402+2(40)(2)+22=1600+160+4=1764. Alternatively, notice that the unit digit is 22=4, which immediately points to either 1504, 1564, 1764, or 1664; checking the tens digit quickly resolves it.
Number to find the square of = 42
(a+b)2=a2+2ab+b2
Use the algebraic expansion identity 422=(40+2)2=402+2(40)(2)+22=1600+160+4=1764. Alternatively, notice that the unit digit is 22=4, which immediately points to either 1504, 1564, 1764, or 1664; checking the tens digit quickly resolves it.
Multiplying incorrectly by rushing manual long multiplication and confusing middle terms (e.g. calculating 1600+4 and forgetting the cross term 2ab=160).
Identify the given number
We need to find the square of the number 42, which means evaluating 422.
422=42├Ч42
Apply algebraic expansion identity
Express 42 as (40+2) and use the binomial square formula (a+b)2=a2+2ab+b2.
(40+2)2=402+2(40)(2)+22
Calculate individual terms
Compute each component: 402=1600, the cross-product 2├Ч40├Ч2=160, and 22=4.
1600+160+4=1764
Match with options
The resulting value is 1764, which matches Option C.
1764
C is correct because the square of 42 is 1764.
Mastering mental binomial expansion techniques helps speed up polynomial simplifications and quadratic equation factorizations in quantitative aptitude.
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