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In algebra, distributing a negative sign can seem tricky at first, but it becomes easy with a bit of practice. When you see a negative sign in front of parenthesis, it means you need to apply it to each term inside those parentheses. This process changes the sign of every term within.

For example, consider the expression \[- (5 - 6y)\]. Here, the negative sign needs to be applied to both terms inside the parentheses. The 5 becomes -5 and the -6y turns into +6y.

• Change positive terms to negative and negative terms to positive.
• Ensure every term inside is affected.

After distributing, the whole expression might look different, but you're one step closer to simplifying it. Keep in mind that distributing the negative sign is an essential step before combining like terms or further simplification.

Combining like terms is a key part of simplifying algebraic expressions. Terms are considered "like" when they have identical variable parts, meaning the variables and their exponents match exactly.

Take, for example, the expression from our exercise: \[-9y + 6y - 5\]. Here, the terms \(-9y\) and \(+6y\) are like terms because they both contain the variable \(y\). We can combine these terms by performing the operation directly on the coefficients (the numbers in front of variables).

• Add or subtract the coefficients.
• Keep the variable part unchanged.

Thus, -9 combined with +6 results in -3, giving us \(-3y\). The expression then reads \(-3y - 5\) after combining. This step is critical for simplifying, as it reduces complexity and brings clarity to what the expression represents.

Simplifying expressions involves both distributing signs and combining like terms, as well as ensuring that no further simplifications are possible. The goal is to reach the simplest form where the expression contains the fewest possible terms.

From the expression \(-3y - 5\), once we've completed the steps of distributing and combining, we check if all similar terms have been combined and there are no common factors to factor out or any terms to cancel. This final form is \(-3y - 5\), with two distinct parts:

• The expression contains one simplified variable term, \(-3y\), representing the algebraic part.
• A constant term, \(-5\), which stands alone without any variable.

This simplified expression is both more concise and easier to interpret, which is useful when substituting values to solve equations or further algebraic operations. Simplification is not just about reducing size; it’s about making expressions clearer and more effective for solving mathematical problems.