To simplify the mathematical expression 4z(5x+3y-1), we use what is known as the distributive property.
The distributive property, in mathematics, is the law which states that multiplication distributes over addition and subtraction. In simpler terms, it means that when a number multiplies a sum of two or more other numbers in parentheses, you can distribute the multiplication across each of the numbers in parentheses and add or subtract the results.
Here is how we can apply it to the given expression:
1. We start with the original expression, 4z(5x+3y-1).
* Note here that z is the number that is distributed among the terms inside the parentheses.
2. Inside the parentheses, we have three terms - 5x, 3y, and -1. Apply the distributive property, we multiply '4z' across each term:
* Multiply 4z by 5x to get 20xz.
* Next, multiply 4z by 3y to get 12yz.
* Lastly, multiply 4z by -1 to get -4z.
3. Final step, we rewrite the entire expression using the results from the above operations:
* We get the expression: 20xz + 12yz - 4z.
So, the property used to simplify the expression 4z(5x+3y-1) is the distributive property.