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When simplifying algebraic expressions, distributing a negative sign is an important first step. A negative sign outside of brackets means every term inside the brackets should change its sign. If a term is positive inside the bracket, it turns negative when preceded by a negative sign. Conversely, a negative term becomes positive.
For example, in the expression \[ 3 - (aZ + 4) \], distributing the negative sign changes it to \[ 3 - aZ - 4 \]. Each term within the brackets has been altered from positive to negative and vice versa.

• The first term \( aZ \) becomes \( -aZ \).
• The second term \( +4 \) becomes \( -4 \).

This ensures that all terms are accurately represented in the next steps of your solution.
Always remember this rule: a negative sign outside the brackets means all the signs inside are flipped.

Combining like terms is crucial to simplifying expressions. Like terms in algebra are terms that have the same variable raised to the same power. They can be combined by simply performing the operations between them.
For instance, consider the terms \( aZ - aZ \). Both contain the same variable \( aZ \), allowing them to be combined easily.

• Collect all the similar terms together.
• Add or subtract the coefficients of these like terms.

In this case, \( aZ - aZ \) results in \( 0 \), as the terms effectively cancel each other out.
This step is key to making the expression shorter and easier to manage.

Simplifying expressions is all about making an algebraic sentence look cleaner and easier to work with. What you need to do is make the expression as short as possible without changing its value. This involves systematically applying rules and operations to reduce the expression.
After distributing the negative sign and combining like terms, as described in previous sections, you often arrive at the simplest form of the expression.
For example, after performing these transformations in our given expression, we end up with \( aZ - aZ + 1 \).

• Cancel zero pairs, like \( aZ - aZ \), resulting in \( 0 \).
• The remaining part of the expression is the simplified version. In our case, it simplifies to \( 1 \).

Each step in this process helps you to streamline the expression to its most basic form.