WHICH ALGEBRAIC PROPERTY OR PROPERTIES ARE ILLUSTRATED BY THE EQUATIONS?
(x+3)^2+0=(x+3)^2
AND
a(x+y)=ax+ay
Well, let's break it down and see which algebraic properties are being illustrated!
For the first equation, (x+3)^2+0=(x+3)^2, the property being illustrated is the additive identity property. This property states that adding zero to any number does not change the value of that number. In this case, adding zero to (x+3)^2 doesn't change the value of (x+3)^2.
Now, for the second equation, a(x+y)=ax+ay, the property being illustrated is the distributive property. This property states that when you multiply a number by a sum or difference, you can distribute the multiplication to each term inside the parentheses. In this case, multiplying a by (x+y) is the same as multiplying a by x and then adding it to a multiplied by y.
So, the properties being illustrated are the additive identity property and the distributive property. Hope that helps, and if not, I'll come juggling to your rescue! 🤡
The equations (x+3)^2+0=(x+3)^2 and a(x+y)=ax+ay illustrate the following algebraic properties:
1. Identity Property of Addition: The equation (x+3)^2+0=(x+3)^2 demonstrates this property. The addition of zero to any number does not change its value.
2. Distributive Property: The equation a(x+y)=ax+ay exemplifies the distributive property. It states that when multiplying a number by the sum of two other numbers, you can distribute the multiplication to each of the terms inside the parentheses.
These are the properties showcased by the given equations.
The equations you provided illustrate different algebraic properties. Let's break them down:
1. (x+3)^2 + 0 = (x+3)^2
This equation illustrates the property of addition identity. The addition identity property states that when you add zero to any number or expression, it remains unchanged. In this equation, adding zero to (x+3)^2 doesn't affect its value, so both sides of the equation remain equal.
2. a(x+y) = ax + ay
This equation illustrates the distributive property. The distributive property states that when you multiply a number or expression by a sum of two or more terms, you can distribute the multiplication to each term and then add or subtract the results. In this equation, a is multiplied by the sum (x+y), and it is distributed to each term, resulting in ax + ay on the right side of the equation.
To identify algebraic properties, it is important to understand the definition and principles behind each property. By recognizing the patterns and rules, you can better analyze and solve equations.