To use the distributive property to write an equivalent expression for [tex]\( 2(m + 2n) \)[/tex], follow these steps:
1. Identify the multiplier: In this expression, the number outside the parentheses is 2, which will be multiplied by each term inside the parentheses.
2. Distribute the multiplier to each term inside the parentheses: There are two terms inside the parentheses: [tex]\( m \)[/tex] and [tex]\( 2n \)[/tex]. The distributive property states that you multiply the term outside the parentheses by each term inside the parentheses.
[tex]\[ 2(m + 2n) = 2 \cdot m + 2 \cdot (2n) \][/tex]
3. Perform the multiplications:
- Multiply 2 by [tex]\( m \)[/tex]:
[tex]\[ 2 \cdot m = 2m \][/tex]
- Multiply 2 by [tex]\( 2n \)[/tex]:
[tex]\[ 2 \cdot (2n) = 4n \][/tex]
4. Combine the results: Add the results of the two multiplications together.
[tex]\[ 2m + 4n \][/tex]
So the expression [tex]\( 2(m + 2n) \)[/tex] is equivalent to [tex]\( 2m + 4n \)[/tex].
