Problem 40 Combine like terms. Write each a... [FREE SOLUTION]

Chapter 15: Problem 40

Combine like terms. Write each answer in descending order. $$ 5 t-8 t^{2}+4 t^{2} $$

Short Answer

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-4t^{2} + 5t

Step by step solution

Identify Like Terms

Find the terms that have the same variables raised to the same power. Here, the like terms are $ -8t^{2} $ and $ 4t^{2} $.

Combine Like Terms

Add or subtract the coefficients of the like terms: $ -8t^{2} + 4t^{2} $. This results in $ -4t^{2} $.

Reorder the Terms

The remaining term is $ 5t $. Write the expression in descending order by the exponent: $ -4t^{2} + 5t $.

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Key Concepts

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

Like Terms

In algebra, like terms are terms that have the same variables raised to the same power. Identifying like terms is crucial when simplifying expressions because only like terms can be combined directly.

For example, in the expression $ 5t - 8t^{2} + 4t^{2} $, we can spot two pairs of like terms:

$ -8t^{2} $ and $ 4t^{2} $
The term $ 5t $ does not have a like term in this particular expression because there's no other term with just $ t $.

Combining like terms simplifies the expression and makes it easier to manage.

Coefficients

Coefficients are the numerical part of the terms that are multiplied by the variable. In the expression $ 5t - 8t^{2} + 4t^{2} $, the coefficients are:

5 in $ 5t $
-8 in $ -8t^{2} $
4 in $ 4t^{2} $

When combining like terms, we add or subtract these coefficients. For the like terms $ -8t^{2} $ and $ 4t^{2} $, we calculate: \[ -8 + 4 = -4 \] This gives us the combined term $ -4t^{2} $. Remember, the variable part stays the same when combining like terms; only the coefficients change.

Descending Order

Descending order in algebra means writing the terms starting with the highest exponent and going down to the lowest. This makes the expression look cleaner and more organized.

In our example, after combining the like terms, we have $ -4t^{2} + 5t $.

The term $ -4t^{2} $ has an exponent of 2, which is higher than the exponent of 1 in $ 5t $. So, we write the expression starting with the term with the largest exponent.

Always remember to check if your final expression is in descending order as this is a standard way of presenting polynomial expressions. So, our final answer in descending order is $ -4t^{2} + 5t $.

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91影视

Combine like terms. Write each answer in descending order. $$ 5 t-8 t^{2}+4 t^{2} $$

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Reorder the Terms

Key Concepts

Like Terms

Coefficients

Descending Order

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