Question
How to expand and find the degree of (8m + 7)(2m + 3)
Answers
GPT-4o mini
To expand the expression \((8m + 7)(2m + 3)\), we can use the distributive property (also known as the FOIL method for binomials). Here's how to do it step-by-step:
1. **Distribute \(8m\)** to both terms in the second binomial:
- \(8m \cdot 2m = 16m^2\)
- \(8m \cdot 3 = 24m\)
2. **Distribute \(7\)** to both terms in the second binomial:
- \(7 \cdot 2m = 14m\)
- \(7 \cdot 3 = 21\)
Now we can combine all the terms together:
\[
16m^2 + 24m + 14m + 21
\]
Next, combine the like terms (\(24m + 14m\)):
\[
16m^2 + 38m + 21
\]
So the expanded expression is:
\[
16m^2 + 38m + 21
\]
To find the degree of the polynomial, we look for the highest power of \(m\) in the expression. The highest power of \(m\) in \(16m^2 + 38m + 21\) is \(m^2\).
Therefore, the degree of the polynomial is:
\[
\text{Degree} = 2
\]
In summary:
- The expanded expression is \(16m^2 + 38m + 21\).
- The degree of the polynomial is \(2\).
1. **Distribute \(8m\)** to both terms in the second binomial:
- \(8m \cdot 2m = 16m^2\)
- \(8m \cdot 3 = 24m\)
2. **Distribute \(7\)** to both terms in the second binomial:
- \(7 \cdot 2m = 14m\)
- \(7 \cdot 3 = 21\)
Now we can combine all the terms together:
\[
16m^2 + 24m + 14m + 21
\]
Next, combine the like terms (\(24m + 14m\)):
\[
16m^2 + 38m + 21
\]
So the expanded expression is:
\[
16m^2 + 38m + 21
\]
To find the degree of the polynomial, we look for the highest power of \(m\) in the expression. The highest power of \(m\) in \(16m^2 + 38m + 21\) is \(m^2\).
Therefore, the degree of the polynomial is:
\[
\text{Degree} = 2
\]
In summary:
- The expanded expression is \(16m^2 + 38m + 21\).
- The degree of the polynomial is \(2\).