Sure, let's break down the given expression [tex]\( w^2 + 5w \)[/tex] and relate each component to the specific descriptions provided.
1. The variable in the expression [tex]\( w^2 + 5w \)[/tex] is [tex]\( w \)[/tex]:
- In the term [tex]\( w^2 \)[/tex], [tex]\( w \)[/tex] is raised to the power of 2.
- In the term [tex]\( 5w \)[/tex], [tex]\( w \)[/tex] has a coefficient of 5.
- Therefore, [tex]\( w \)[/tex] is the variable in both parts of the expression.
Pair: the [tex]\( w \)[/tex] in [tex]\( w^2 + 5w \)[/tex]
2. The exponent in the term [tex]\( w^2 \)[/tex]:
- Here [tex]\( w \)[/tex] is raised to the power of 2, which makes the exponent 2.
Pair: the 2 in [tex]\( w^2 + 5w \)[/tex]
3. The coefficient in the term [tex]\( 5w \)[/tex]:
- In this term, [tex]\( w \)[/tex] is multiplied by 5. Here, 5 is the coefficient of [tex]\( w \)[/tex].
Pair: the 5 in [tex]\( w^2 + 5w \)[/tex]
4. The two terms in the expression [tex]\( w^2 + 5w \)[/tex]:
- The expression consists of two separate terms: [tex]\( w^2 \)[/tex] and [tex]\( 5w \)[/tex].
Pair: the [tex]\( w^2 \)[/tex] or the [tex]\( 5w \)[/tex] in [tex]\( w^2 + 5w \)[/tex]
Now, let's list the pairs together as an answer:
- the [tex]\( w \)[/tex] in [tex]\( w^2 + 5w \)[/tex] pairs with [tex]\( w \)[/tex].
- the 2 in [tex]\( w^2 + 5w \)[/tex] pairs with the exponent 2.
- the 5 in [tex]\( w^2 + 5w \)[/tex] pairs with the coefficient 5.
- the [tex]\( w^2 \)[/tex] or the [tex]\( 5w \)[/tex] in [tex]\( w^2 + 5w \)[/tex] pairs with the terms [tex]\( w^2 \)[/tex] and [tex]\( 5w \)[/tex].
The detailed breakdown yields this pair association:
[tex]\[
(w^2+5w \quad \text{pairs with}) \\
\begin{aligned}
& \text{the } w \quad \text{in } w^2 + 5w \quad \text{pairs with}\quad w,\\
& \text{the } 2 \quad \text{in } w^2 + 5w \quad \text{pairs with}\quad 2,\\
& \text{the } 5 \quad \text{in } w^2 + 5w \quad \text{pairs with}\quad 5,\\
& \text{the } w^2 \quad \text{or the } 5w \quad \text{in } w^2 + 5w \quad \text{pairs with}\quad [w^2, 5w].
\end{aligned}
\][/tex]
