Additive Identity Property
2026-02-28 12:56 Diff
https://brightchamps.com/en-us/math/numbers/additive-identity-property

Additive identity property can be applied to all kinds of numbers. Here, we will look at how it can be used in math equations:  

Additive Identity in Algebra


The additive identity property can be applied to any algebraic expression, as adding a zero to such an expression will not affect its value.


For example, let’s try adding 0 to the algebraic expression,

\(6y + 3 \)


\((6y + 3) + 0 = 6y + 3 \)


This proves that the additive identity property works in algebra.

Additive Identity in Equations


The additive identity (0) plays a key role in solving equations, as it helps maintain the balance of the equation. In an equation, whenever we add or subtract a number from one side, the same must be done on the other side to maintain balance. This is done to solve for unknown variables.

This can be better understood with an example. 


\(4x - 6 = 6 \)


Adding 6 to both sides eliminates the constant term on the left, helping to solve for the unknown variable x. So let’s add 6 on both sides.


\(4x – 6 + 6 = 6 + 6 \)


\(4x = 12 \)


\(x = \frac{12}{4} = 3 \)


This is how additive identity property can be used to solve equations.

Additive Identity in Polynomials


When we add or subtract the zero polynomial, which has all coefficients equal to zero, from any polynomial, it does not change the polynomial’s degree or its coefficients. This idea can be used while simplifying polynomials, performing polynomial operations, and solving equations.

For example, adding the zero polynomial (0) to \(5x^2 + 2x - 3 \) does not change or affect the polynomial. Here, the polynomial \(5x^2 + 2x - 3 \) remains the same.