Final answer:
The example of the distributive property is option c) 3(10+5) = 30 + 15. It demonstrates multiplying a single term outside the parentheses by each term inside, showcasing one of the fundamental properties in algebra which links addition and multiplication.
Step-by-step explanation:
The distributive property in mathematics allows you to multiply a single term by each term within a set of parentheses. The correct example of the distributive property from the options provided is c) 3(10+5) = 30 + 15. This shows that 3 is multiplied by each number within the parentheses individually (3 x 10) + (3 x 5), which equals 30 + 15.
The distributive property is used frequently in algebra to simplify expressions and solve equations. It's a fundamental property that links addition and multiplication in a way that allows for these operations to be performed more efficiently. When you master this property, you'll find it easier to work with algebraic expressions and solve problems.
Some common mistakes might include misapplying the distributive property or misconstruing it with the commutative property or the associative property. However, remember that the distributive property is unique in that it involves both addition and multiplication, unlike the commutative property which is only for addition or multiplication and the associative property which allows you to change grouping in expressions.