Problem 31 Add $$(-p+16)+(-7 p-9)$$... [FREE SOLUTION]

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Chapter 6: Problem 31

Add $$(-p+16)+(-7 p-9)$$

Short Answer

Expert verified

The short answer to the given question 'Add $(-p+16)+(-7 p-9)$' is: $-8p + 7$.

Step by step solution

Write down the given expressions

Write down the given expressions that need to be added, which are $(-p+16)$ and $(-7p-9)$.

Remove the parentheses

Since there are no coefficients to distribute inside the parentheses, simply remove them and combine the expressions: \[-p + 16 - 7p - 9\]

Identify and combine like terms

Identify like terms as those with the same variable (p) and the constants. In this case, the terms $-p$ and $-7p$ are like terms, as well as the constants $16$ and $-9$. Combine the like terms by performing the necessary operations: \[-p - 7p + 16 - 9\]

Solve

Now solve for the combined expressions: \[(-1 - 7)p + (16 -9)\] Which simplifies to: \[-8p + 7\]

Write the final answer

As the result, the sum of the given expressions $(-p+16)+(-7p-9)$ is $-8p + 7$.

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Key Concepts

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

Combining Like Terms

Combining like terms is an essential skill in algebra for simplifying expressions. Like terms are terms that have the same variable raised to the same power. In our exercise, the terms $-p$ and $-7p$ are like terms because they both have the variable $p$ raised to the same power. You can only combine these similar terms effectively.

To combine them, simply add or subtract their coefficients. In this example, $-1$ and $-7$ are the coefficients of $p$. Hence, combining these terms is done by calculating:

$-1 - 7 = -8$

Now you have the expression $-8p$. Always keep an eye out for like terms in any problem, as they help simplify expressions without changing their value.

Polynomial Addition

Polynomial addition involves adding two or more polynomials. Each polynomial can have multiple terms, and your goal is to combine them efficiently. Here, we're adding $(-p + 16)$ and $(-7p - 9)$.

Before starting, it's important to write the polynomials neatly, lining up like terms. In this case:

Line up terms with $p$ together and constant terms together.
Make sure no terms are missing from the lineup.

Remove parentheses and group similar terms together:\[-p + 16 - 7p - 9\]

Now, you can easily see which terms to combine. This setup makes the process clear and prevents errors. Always verify each term is correctly added to its like counterpart.

Simplifying Expressions

Simplifying an expression is the process of rewriting it in its most concise form while maintaining its value. This involves combining like terms and performing all possible operations.

In our exercise:

Combine the $p$ terms: $-p - 7p = -8p$
Combine the constants: $16 - 9 = 7$

The expression simplifies to $-8p + 7$.

This simplified form is cleaner and often more useful for further calculations or understanding the relationship between variables. Remember, simplifying doesn鈥檛 change the value of the expression鈥攊t only makes it easier to handle and understand.

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91影视

Add $$(-p+16)+(-7 p-9)$$

Short Answer

Step by step solution

Write down the given expressions

Remove the parentheses

Identify and combine like terms

Solve

Write the final answer

Key Concepts

Combining Like Terms

Polynomial Addition

Simplifying Expressions

One App. One Place for Learning.

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