To find an equivalent expression for the sum of 7a²b, 10a²b², and 14a²b³, we must first factor out any common terms shared by these expressions. Let’s analyze them one at a time:
- The first term is 7a²b. It consists of the factors 7, a², and b.
- The second term is 10a²b². Here we have factors of 10, a², and b².
- The third term is 14a²b³, consisting of 14, a², and b³.
After examining these expressions, we can see that the common factors across all three terms are a². Therefore, we factor a² out of each term:
Now we can rewrite the expression:
- First term: 7a²b = a²(7b)
- Second term: 10a²b² = a²(10b²)
- Third term: 14a²b³ = a²(14b³)
Consequently, the entire sum can be expressed as:
7a²b + 10a²b² + 14a²b³ = a²(7b + 10b² + 14b³)
Now we look for any common factors in the sum (7b + 10b² + 14b³), and we can observe that there are no common terms across b, b², and b³ that can be factored out further.
Therefore, the final equivalent expression is:
7a²b + 10a²b² + 14a²b³ = a²(7b + 10b² + 14b³)
In summary, the expression equivalent to the sum of 7a²b, 10a²b², and 14a²b³ is a²(7b + 10b² + 14b³).