An expression that equivalent to 12x + 8
The Correct Answer and Explanation is:
To find an expression equivalent to ( 12x + 8 ), we can factor the expression. The goal is to express ( 12x + 8 ) in a different, but equivalent, form. Let’s go through the steps to achieve this:
Step 1: Identify common factors
Look for a common factor in both terms of the expression. The two terms are ( 12x ) and ( 8 ).
- ( 12x ) can be broken down as ( 12 \cdot x ).
- ( 8 ) can be written as ( 2 \cdot 4 ) or just ( 8 ).
The greatest common factor (GCF) between 12 and 8 is 4, because 4 is the largest number that divides both 12 and 8 evenly.
Step 2: Factor out the GCF
Now, we factor out the common factor of 4 from both terms of the expression:
[
12x + 8 = 4(3x + 2)
]
Step 3: Verify the factorization
To check if the factorization is correct, we can distribute the 4 back into the parentheses:
[
4(3x + 2) = 4 \cdot 3x + 4 \cdot 2 = 12x + 8
]
This confirms that the factored form, ( 4(3x + 2) ), is indeed equivalent to the original expression ( 12x + 8 ).
Step 4: Conclusion
Therefore, an expression equivalent to ( 12x + 8 ) is ( 4(3x + 2) ).
This method of factoring is useful because it allows us to express the original expression in a more simplified form that might be easier to manipulate in algebraic operations. Factoring out the greatest common factor is often a helpful first step in solving algebraic problems, as it simplifies expressions and can make further operations easier.