Find the squares of the following numbers using the identity `(a+b)^2=a^2 +2a b+b^2:` (I)405 (ii) 510 (iii) 1001 (iv)209 (v) 605

Explanation

To find the squares of the given numbers using the identity \((a + b)^2 = a^2 + 2ab + b^2\), we will break each number into two parts, \(a\) and \(b\), where \(a\) is a round number and \(b\) is the remaining part. Let's solve each part step by step.

### (I) Find the square of 405

1. **Break down the number**:
\[ 405 = 400 + 5 \]
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