To calculate \( 17 \times 17 \) using the breakdown method, we can break it down into more manageable parts.
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Break down 17:
- \( 17 = 10 + 7 \)
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Set up the multiplication:
- \( 17 \times 17 = (10 + 7) \times (10 + 7) \)
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Apply the distributive property (also known as the FOIL method): \[ (10 + 7) \times (10 + 7) = 10 \times 10 + 10 \times 7 + 7 \times 10 + 7 \times 7 \]
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Calculate each term:
- \( 10 \times 10 = 100 \)
- \( 10 \times 7 = 70 \)
- \( 7 \times 10 = 70 \)
- \( 7 \times 7 = 49 \)
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Add all the products together: \[ 100 + 70 + 70 + 49 \]
- First, add the tens: \( 100 + 70 + 70 = 240 \)
- Then, add the last term: \( 240 + 49 = 289 \)
So, \( 17 \times 17 = 289 \).