91Ó°ÊÓ

In algebra, the distributive property is a useful tool to simplify expressions and solve equations. It allows you to distribute a number or variable across terms within parentheses. For example, in the expression \(a(b + c)\), you apply the distributive property to get \(ab + ac\).

In our exercise, we distribute the negative sign. When we have the expression \(n^2 - 6m - (-n^2 - 2m)\), we need to apply the distributive property to the negative sign before the parentheses. This changes the signs inside the parentheses, leading to \(n^2 - 6m + n^2 + 2m\).

Remember, distributing a negative sign essentially flips the sign of every term inside the parentheses. This is an important step in working towards algebraic simplification.

Like terms in algebra are terms that contain the same variables raised to the same power. For example, \(3x\) and \(5x\) are like terms because both have the variable \(x\). Low. However, \(3x\) and \(3y\) are not like terms because the variables are different.

In our exercise, we combine like terms after applying the distributive property. After simplification, the expression is \(n^2 - 6m + n^2 + 2m\). Here, \(n^2\) and \(n^2\) are like terms, while \(-6m\) and \(+2m\) are also like terms.

Combining like terms means adding or subtracting their coefficients. In our case, \(n^2 + n^2 = 2n^2\) and \(-6m + 2m = -4m\). Simplifying like terms is crucial in reducing algebraic expressions.

Algebraic simplification involves reducing an expression to its simplest form. This often requires applying the distributive property and combining like terms.

In our exercise, we started with \(n^2 - 6m - (-n^2 - 2m)\). After distributing the negative sign and combining like terms, we get \(2n^2 - 4m\).

To simplify effectively:

• Distribute any constants or variables across terms inside parentheses.
• Identify and combine like terms by adding or subtracting their coefficients.
• Rewrite the expression to reflect these changes.

By simplifying expressions, we make them easier to work with and solve, especially in more complex equations or functions.