Problem 746 Simplify. $$ -22 p+17 q+(-35... [FREE SOLUTION]

Chapter 1: Problem 746

Simplify. $$ -22 p+17 q+(-35 p)+(-27 q) $$

Short Answer

Expert verified

-57p - 10q

Step by step solution

Identify like terms

Group the terms with the variable 'p' together and the terms with the variable 'q' together. In this case, -22p and -35p are like terms, and 17q and -27q are like terms.

Combine like terms for 'p'

Add the coefficients of the terms with 'p': -22p + (-35p) = -57p.

Combine like terms for 'q'

Add the coefficients of the terms with 'q': 17q + (-27q) = -10q.

Write the simplified expression

Combine the results from the previous steps to write the simplified expression: -57p - 10q.

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Key Concepts

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

Combining Like Terms

When simplifying algebraic expressions, one of the foundational techniques is combining like terms.
Like terms are terms that have the same variables raised to the same power, but can have different coefficients.
In the given exercise, -22p and -35p are like terms because both include the variable 'p'. Similarly, 17q and -27q are like terms as they both include the variable 'q'.
Combining like terms makes the expression simpler and easier to work with in further calculations.

Coefficients

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression.
In our exercise, -22 is the coefficient of the term -22p, and 17 is the coefficient of the term 17q.
When combining like terms, we actually combine their coefficients.
For example, to combine -22p and -35p, we add their coefficients -22 and -35, resulting in -57p.
This is crucial for simplifying expressions and solving equations.

Variables

A variable is a symbol used to represent a number in expressions or equations.
Variables can stand for different numbers at different times.
In the given exercise, 'p' and 'q' are the variables. Identifying which terms share the same variable is important for combining like terms.
Remember that only terms with the same variables can be combined.
For example, 'p' terms are combined separately from 'q' terms to simplify the expression properly.
This understanding helps you manipulate and solve algebraic expressions more efficiently.

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91影视

Simplify. $$ -22 p+17 q+(-35 p)+(-27 q) $$

Short Answer

Step by step solution

Identify like terms

Combine like terms for 'p'

Combine like terms for 'q'

Write the simplified expression

Key Concepts

Combining Like Terms

Coefficients

Variables

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