Problem 21 Combine like terms. $$-8 p^{2}... [FREE SOLUTION]

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Prealgebra

Julie Miller, Molly O鈥橬eill, Nancy Hyde

$Math Studyset 91影视 Explanations$ Math

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Chapter 10: Problem 21

Combine like terms. $$-8 p^{2}-2 p^{2}$$

Short Answer

Expert verified

-10p^2

Step by step solution

- Identify Like Terms

Look at the terms provided: $-8p^2$ and $-2p^2$. Both terms are like terms because they both contain the same variable raised to the same power, which is $p^2$.

- Combine the Coefficients

Add the coefficients of the like terms together. The coefficients are $-8$ and $-2$. Adding them together:$-8 + (-2) = -10$

- Attach the Variable Part

After combining the coefficients, attach the variable part $p^2$ to the result obtained from adding the coefficients. So, $-10$ combined with $p^2$ gives:$-10p^2$

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Key Concepts

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

Combining Like Terms

When combining like terms, look at the coefficients, which are the numbers in front of the variables. Then, add or subtract these coefficients while keeping the variable part unchanged.

Coefficients

In the given problem, we have coefficients $ -8 $ and $ -2 $. To combine these like terms, add the coefficients together: $ -8 + (-2) = -10 $. Remember, when working with negative coefficients, treat the plus and minus signs carefully.

Variable Powers

In the example, both $ -8p^2 $ and $ -2p^2 $ have $ p $ raised to the same power, making them like terms. If the powers were different, we wouldn't be able to combine them directly.

Simplifying Expressions

Remember that simplifying expressions helps in solving equations more efficiently and clarifying mathematical relationships.

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91影视

Combine like terms. $$-8 p^{2}-2 p^{2}$$

Short Answer

Step by step solution

- Identify Like Terms

- Combine the Coefficients

- Attach the Variable Part

Key Concepts

Combining Like Terms

Coefficients

Variable Powers

Simplifying Expressions

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