Which property is illustrated by the equation:
ax+ay=a(x+y)
a x + a y = a ( x + y )
a ( x + y ) = a ( x + y )
Identity
ax+ay=a(x+y)
identify
The property illustrated by the equation "ax + ay = a(x + y)" is the distributive property.
To understand this property, let's break down the equation step by step:
1. Start with the left side of the equation, which is "ax + ay."
- In this expression, 'a' is a coefficient, and 'x' and 'y' are variables.
2. Next, let's consider the right side of the equation, which is "a(x + y)."
- In this expression, 'a' is a coefficient, and 'x + y' is a sum inside parentheses.
The distributive property states that when you multiply a term by a sum inside parentheses, you can distribute the multiplication to each term inside the parentheses.
So, in the given equation, 'a' is being distributed to 'x' and 'y' separately, resulting in the same expression on both sides of the equation.
In simpler terms, the distributive property shows that multiplying a number by the sum of two values is the same as multiplying the number by each value separately and then adding the results together.
This property is fundamental in algebra and is often used to simplify and solve equations.