91Ó°ÊÓ

In algebra, simplifying expressions is often the first step towards solving complex equations. Understanding the distributive property helps to break this down.

The distributive property states that for any numbers or variables, \(a(b+c) = ab + ac\).

In our given exercise, we have the expression \(8a - (3a + 4) - (5a - 3)\). To simplify it, we need to distribute the negative signs:

First, we rewrite the expression:
\(8a - (3a + 4) - (5a - 3)\).

Applying the distributive property, we distribute the negative signs across the terms inside the parentheses:
\(8a - 3a - 4 - 5a + 3\). This step helps to eliminate parentheses, making combining like terms easier.

Let's move forward to see how combining like terms works after distributing.

Once the distributive property is applied, simplifying expressions involves combining like terms and constants.

From the previous step, we had the simplified expression:
\(8a - 3a - 4 - 5a + 3\).

First, let's group and simplify the terms with the variable 'a':
\(8a, -3a, -5a\).

Adding these together, we get:
\((8 - 3 - 5)a = 0a\).

Next, we handle the constant terms, which are -4 and +3:

Combining these, we get: \(-4 + 3 = -1\).

Simplifying an algebraic expression requires careful attention to both the variable and constant terms. Let’s discuss combining like terms next!

Combining like terms means grouping terms in an algebraic expression that have identical variable parts.

Returning to our expression after distributing the negative signs:
\(8a - 3a - 4 - 5a + 3\).

We already saw how the terms with 'a' were combined:

• \8a \
  
• \-3a \
  
• \-5a \
  

All terms involving 'a' are like terms, and their coefficients are added. Thus, \(8 - 3 - 5\) results in \0a\.

Similarly, the constants are also like terms:

• \-4 \
  
• \+3 \

Combining them results in -1.

Putting this all together: \(0a - 1\) simplifies to \ -1 \. Combining like terms streamlines algebraic expressions, revealing simpler forms that are easier to work with in further problem-solving.