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Chapter 10: Problem 2

Apply the distributive property and combine like terms. \(-4(3 t-w)+5(t+2 w)\)

Short Answer

Expert verified
-7t + 14w

Step by step solution

01

- Apply the Distributive Property

Distribute (-4) to each term inside the first parenthesis: -4(3t) - 4(-w) = -12t + 4w. Then distribute 5to each term inside the second parenthesis: 5(t) + 5(2w) = 5t + 10w.
02

- Write the Expanded Form

Combine the results from the distribution: -12t + 4w + 5t + 10w.
03

- Combine Like Terms

Combine the like terms (-12t + 5t) to get -7t and combine (4w + 10w) to get 14w.
04

- Write the Final Result

The simplified expression after combining like terms is -7t + 14w.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Combine Like Terms
Combining like terms is a foundational concept in prealgebra and algebra. It involves summing up terms that have the same variable raised to the same power.

For example, in the expression \(-4(3 t-w)+5(t+2 w)\), after distributing, you get:
  • -12t
  • +4w
  • +5t
  • +10w

The goal is to combine terms that are alike. Terms are considered alike if they contain the same variable to the same power. In our case:
  • \

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Most popular questions from this chapter

Which is greater? \(\left(2^{3}\right)^{2}\) or \(\left(2^{2}\right)^{3}\)

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