Simplify the expression a + g(3 + b) + 3b.
Understand the Problem
The question involves simplifying the expression given: a + g(3 + b) + 3b. This is a typical algebraic manipulation problem where we will combine like terms and distribute where necessary.
Answer
The simplified expression is \( a + 3g + gb + 3b \).
Answer for screen readers
The simplified expression is ( a + 3g + gb + 3b ).
Steps to Solve
- Distribute the term g We start with the expression ( a + g(3 + b) + 3b ). To simplify it, we apply the distributive property to the term ( g(3 + b) ):
$$ g(3 + b) = 3g + gb $$
So we can rewrite the expression as:
$$ a + 3g + gb + 3b $$
- Combine like terms Next, we look for like terms in the expression ( a + 3g + gb + 3b ). Since ( a ), ( 3g ), ( gb ), and ( 3b ) do not have any additional like terms, we cannot combine any further.
Thus, the simplified expression remains:
$$ a + 3g + gb + 3b $$
- Final Form The final step presents the expression clearly. Therefore, the result from combining terms is:
$$ a + 3g + bg + 3b $$
The simplified expression is ( a + 3g + gb + 3b ).
More Information
This type of problem demonstrates how to apply the distributive property and combine like terms effectively in algebra. Each step helps to clarify the structure of the expression, leading to a clearer final result.
Tips
- Forgetting to distribute ( g ) to both terms in ( (3 + b) ). Make sure to distribute to all components within the parentheses.
- Not recognizing that all terms need to be kept separate since they are not like terms.
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