Explanation:

Distributive Property:
- When we have a number outside parentheses multiplied by a sum inside the parentheses, we can distribute the number to each term inside the parentheses.

Given Equation:
- We are given the equation 13×(100-19)=(13×100)-(13×19).

Step 1:
- Simplify the expression inside the parentheses first: 100-19 = 81.

Step 2:
- Substitute the simplified expression back into the original equation: 13×81 = (13×100)-(13×19).

Step 3:
- Multiply 13 by 81 to get 1053 on the left side of the equation.

Step 4:
- Multiply 13 by 100 to get 1300 and multiply 13 by 19 to get 247 on the right side of the equation.

Step 5:
- Therefore, the equation becomes 1053 = (1300)-(247).

Step 6:
- Subtract 247 from 1300 to get the left side equal to 1053.

Step 7:
- Thus, 1053 = 1053.

Conclusion:
- By applying the distributive property and simplifying both sides of the equation, we have shown that the given equation is true.