Rewrite the expression in the form of 5n. 5(-5) + 5(8)

Answer: To rewrite the expression in the form of 5n, we can use the distributive property of multiplication over addition. Let's do this step by step:

The original expression is: 5(-5) + 5(8)

Using the distributive property, we can factor out the common factor, which is 5 in this case:

5(-5 + 8)

Now we just need to perform the addition inside the parentheses:

5(-5 + 8) = 5(3)

So, the expression in the form of 5n, where n is an integer, is 5(3) or simply 15, since 5 times 3 equals 15. We can say that n is equal to 3 in this case.

Extra: The distributive property is one of the basic properties of numbers, and it allows us to multiply a number by a sum or difference by multiplying each addend or subtrahend separately and then adding the results. This property is useful in simplifying algebraic expressions and solving equations. In general, the distributive property can be expressed as a(b + c) = ab + ac or a(b - c) = ab - ac, where a, b, and c are numbers. This property is essential for understanding how to manipulate and simplify expressions in algebra.