To solve \(13 \times 17\) in expanded form, we can fill in the blanks as follows:
We start with the expression: \[ (10 + 3) \times (10 + 7) \] We can expand this using the distributive property: \[ (10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7) \] Now, let's calculate each part:
- \(10 \times 10 = 100\)
- \(10 \times 7 = 70\)
- \(3 \times 10 = 30\)
- \(3 \times 7 = 21\)
So, we replace the question marks: \[ (10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7) = 100 + 70 + 30 + 21 \]
Thus, filling in the blanks, we get: \[ (10 + 3) \times (10 + 7) = (10 \times 10) + (10 \times 7) + (3 \times 10) + (3 \times 7) \implies 100 + 70 + 30 + 21 \]
Finally, when you add these all together: \[ 100 + 70 + 30 + 21 = 221 \]
So, the answer to fill in the blanks is \(30\) for the missing value in the expression.