Which of the expressions is equivalent to the expression?
6mn+m3n+9n2
To solve the problem, we'll follow these steps:
- Step 1: Identify the common factor in the expression 6mn+m3n+9n2.
- Step 2: Factor this common factor out from the expression.
- Step 3: Compare the factored expression to the given choices.
Let's work through each step:
Step 1: Identify the Common Factor
Looking at the terms 6mn, m3n, and 9n2, the common factor among them is clearly 3n since:
- 6mn can be divided by 3n, giving 2m.
- m3n can be divided by 3n, giving m1.
- 9n2 can be divided by 3n, giving 3n.
Step 2: Factor Out the Common Factor
Factoring 3n out of each term, we rewrite the expression:
6mn+m3n+9n2=3n(2m)+3n(m1)+3n(3n).
This simplifies to:
3n(2m+m1+3n).
Step 3: Compare with Choices
We compare our factored expression, 3n(2m+m1+3n), to the given choices. We find that Choice 1 matches our factored form.
Therefore, the expression 6mn+m3n+9n2 is equivalent to 3n(2m+m1+3n).
3n(2m+m1+3n)