Can you use the distributive property in absolute values?

Answer 1

Yes, you can apply the distributive property in expressions involving absolute values, but it's important to consider the properties of absolute values. The distributive property states that ( a(b + c) = ab + ac ), and this can be used with absolute values, such as ( |a(b + c)| = |ab + ac| ). However, the absolute value of a sum is not necessarily equal to the sum of the absolute values, meaning ( |a + b| \neq |a| + |b| ) in general. Thus, careful attention is needed when manipulating expressions involving absolute values.