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Which property is illustrated by the equation ax+ay=a(x+y)?

Question:

Which property is illustrated by the equation {eq}\ ax+ay=a(x+y) {/eq}?

Properties of Equality in Mathematics:

There are a number of different properties within the study of mathematics. One group of properties is called the properties of equality, and these properties give equations that show that two mathematical expressions are equal for any values of the variables in the equations.

Answer and Explanation:

The property illustrated by the equation ax + ay = a(x + y) is the distributive property of equality. The distributive property of equality states that if A, B, and C are mathematical expressions, then A(B + C) = AB + AC. We see that if we reverse this property, then we get that AB + AC = A(B + C), and this is the exact property that we are given with ax + ay = a(x + y). Therefore, the property illustrated by the equation ax + ay = a(x + y) is the distributive property of equality.


Learn more about this topic:

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Distributive Property: Definition, Use & Examples

from High School Algebra II: Help and Review

Chapter 2 / Lesson 20
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