17 x 17 using breakdown method

1 answer

To calculate \( 17 \times 17 \) using the breakdown method, we can break it down into more manageable parts.

  1. Break down 17:

    • \( 17 = 10 + 7 \)
  2. Set up the multiplication:

    • \( 17 \times 17 = (10 + 7) \times (10 + 7) \)
  3. Apply the distributive property (also known as the FOIL method): \[ (10 + 7) \times (10 + 7) = 10 \times 10 + 10 \times 7 + 7 \times 10 + 7 \times 7 \]

  4. Calculate each term:

    • \( 10 \times 10 = 100 \)
    • \( 10 \times 7 = 70 \)
    • \( 7 \times 10 = 70 \)
    • \( 7 \times 7 = 49 \)
  5. 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, \( 17 \times 17 = 289 \).