Evaluate $42^{2}$

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Solution

Use: ${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$
Given $42^{2}$
Since, $42^{2}$ can be written as ${(40 + 2)}^{2}$
So, applying
${(a + b)}^{2} = a^{2} + b^{2} + 2 a b$ , we get
${(40 + 2)}^{2} = 40^{2} + 2^{2} + 2 (40) (2) = 1600 + 4 + 160 = 1764$
Hence, $42^{2}$ is equal to $1764$ .

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