Use the rectangle below to prove that \((a+b)^2=a^2+2ab+b^2\). (3 marks)
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| \(\text{Length of large rectangle}\) | \(=a+b\) |
| \(\text{Width of large rectangle}\) | \(=a+b\) |
| \(\text{Area of large rectangle}\) | \(=(a+b)\times(a+b)\) |
| \(=(a+b)^2\) |
| \(\text{Adding 4 areas inside large rectangle}\) | \(=a^2+a\times b+a\times b+b^2\) |
| \(=a^2+2ab+b^2\) |
\(\therefore (a+b)^2=a^2+2ab+b^2\)