Combine like terms: $3 u-8 v+2 w-5 u+8 v-w$

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gracielabara332 gracielabara332

06-11-2026
Mathematics

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Combine like terms: $3 u-8 v+2 w-5 u+8 v-w$

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-06T18:36:31-05:00

Identify terms with the same variable: $u$-terms are $3u, -5u$; $v$-terms are $-8v, 8v$; $w$-terms are $2w, -w$.
Add the coefficients for each group: $(3-5)u = -2u$, $(-8+8)v = 0$, and $(2-1)w = w$.
Combine the simplified terms to get the final expression.
The final simplified expression is $\boxed{{-2u+w}}$.

Explanation

Identifying and Grouping Like Terms

To simplify the expression $3u - 8v + 2w - 5u + 8v - w$, we need to identify and group the like terms. Like terms are terms that share the same variable raised to the same power. In this expression, we have three types of variables: $u$, $v$, and $w$. Our goal is to collect all terms associated with each specific variable and combine their coefficients.

Combining the Coefficients

First, we group the terms containing $u$: $3u$ and $-5u$. Combining their coefficients gives $3u - 5u = (3 - 5)u = -2u$. Next, we group the terms containing $v$: $-8v$ and $8v$. Combining their coefficients gives $-8v + 8v = (-8 + 8)v = 0v = 0$. Finally, we group the terms containing $w$: $2w$ and $-w$. Combining their coefficients gives $2w - w = (2 - 1)w = 1w = w$.

Final Simplification

Now that we have simplified each variable group separately, we can write the final simplified expression by adding the results together: $-2u + 0 + w = -2u + w$. Thus, the simplified expression is $-2u + w$.

Examples

Combining like terms is similar to sorting different types of items before counting them. For instance, if you have a pile of fruits containing 3 apples and 5 oranges ($3a + 5o$) and you add another 2 apples and take away 3 oranges ($+ 2a - 3o$), you can determine your total by grouping the fruits: $(3+2)a + (5-3)o = 5a + 2o$. This simple algebraic grouping helps in organizing data and simplifying complex mathematical expressions into manageable forms.