Which property is demonstrated by the equation ax(b+c) = axb + axc?

The equation ( ax(b+c) = axb + axc ) demonstrates the distributive property. This property states that when you multiply a number by a sum, you can distribute the multiplication to each addend within the parentheses.

In this case, ( a ) is multiplied by the sum of ( b ) and ( c ). The correct application of the distributive property allows you to rewrite this expression as the sum of two products: ( axb ) (where ( a ) is multiplied by ( b )) and ( axc ) (where ( a ) is multiplied by ( c )). Therefore, this equation illustrates the process of distributing the multiplication across the addition inside the parentheses, which is the essence of the distributive property.

Understanding this property is fundamental in mathematics because it helps simplify expressions and solve equations involving addition and multiplication efficiently.