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(1012)^(2)...

`(1012)^(2)`

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To solve the expression \( (1012)^2 \), we can use the formula for squaring a binomial, which is \( (a + b)^2 = a^2 + 2ab + b^2 \). Here, we can break down \( 1012 \) into \( 1000 + 12 \). ### Step-by-Step Solution: 1. **Identify \( a \) and \( b \)**: Let \( a = 1000 \) and \( b = 12 \). 2. **Calculate \( a^2 \)**: \[ a^2 = (1000)^2 = 1000000 \] 3. **Calculate \( b^2 \)**: \[ b^2 = (12)^2 = 144 \] 4. **Calculate \( 2ab \)**: \[ 2ab = 2 \times 1000 \times 12 = 24000 \] 5. **Combine the results**: Now, we add all the calculated values together: \[ (1012)^2 = a^2 + 2ab + b^2 = 1000000 + 24000 + 144 \] 6. **Perform the addition**: \[ 1000000 + 24000 = 1024000 \] \[ 1024000 + 144 = 1024144 \] Thus, the final answer is: \[ (1012)^2 = 1024144 \]
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