Use the distributive property to fill in the blanks below. \[ 7 \times(3+8)=(7 \times \square)+(7 \times \square) \]

Step 1 ：Given the equation \(7 \times(3+8)=(7 \times \square)+(7 \times \square)\), we need to fill in the blanks using the distributive property.

Step 2 ：The distributive property states that the product of a number and the sum of two or more numbers is equal to the sum of the products of the number and each addend.

Step 3 ：In this case, the number is 7 and the addends are 3 and 8.

Step 4 ：Therefore, the blanks should be filled with 3 and 8 respectively.

Step 5 ：Substituting these values into the equation, we get \(7 \times(3+8)=(7 \times 3)+(7 \times 8)\).

Step 6 ：\(\boxed{7 \times(3+8)=(7 \times 3)+(7 \times 8)}\) is the final answer.