Is the product of 9 and twice m translated 9(2m) or 9(m+m)?
yes.
The two expressions are equivalent, since m+m = 2m
That said, I'd interpret
"product of 9 and twice m" as 9(2m)
and
"product of 9 and the sum of m and m" as 9(m+m)
That would leave open the possibility of something like
"product of 9 and the sum of m and k" as 9(m+k)
The product of 9 and twice m can be expressed as 9(2m). To understand why, let's break it down step by step:
First, we have the variable m. When we say "twice m," we mean 2 times the value of m.
So, "twice m" can be written as 2m.
Next, we want to find the product of 9 and twice m. To multiply these two expressions, we use the distributive property. According to the distributive property, when we have a number (in this case, 9) multiplied by an expression enclosed in parentheses (in this case, 2m), we can distribute the multiplication to each term within the parentheses.
So, 9 multiplied by 2m can be written as 9 * 2 * m, which simplifies to 18m.
Therefore, the product of 9 and twice m is 18m, and it can be correctly written as 9(2m).