Problem 2 $7 y^{2}+5-9 y^{2}-8$... [FREE SOLUTION]

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Elementary Algebra

Laura Bracken, Ed Miller

$Math Studyset 91影视 Explanations$ Math

1 Edition

Chapter 5: Problem 2

$7 y^{2}+5-9 y^{2}-8$

Short Answer

Expert verified

-2y^2 - 3

Step by step solution

Identify Like Terms

Identify the like terms in the equation. Here, the terms involving $y^2$ are $7y^2$ and $-9y^2$. The constant terms are $+5$ and $-8$.

Combine Like Terms

Combine the like terms. First, combine the terms involving $y^2$: $7y^2 - 9y^2 = -2y^2$. Next, combine the constants: $5 - 8 = -3$.

Write the Simplified Expression

After combining the like terms, write the simplified expression: $-2y^2 - 3$.

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Key Concepts

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

like terms

When working with algebraic expressions, it's essential to understand 'like terms'.
Like terms are terms that have the same variables raised to the same powers, although their coefficients can be different.
For example, in the expression given above, the terms involving $ y^2 $ such as $ 7y^2 $ and $ -9y^2 $ are like terms.
Similarly, constants like 5 and -8 are like terms because they do not have any variables.
Always look for like terms first when simplifying an expression. This will help you organize and combine terms accurately.

combining like terms

Once you've identified like terms, the next step is to combine them.
This means adding or subtracting the coefficients of the like terms.
In our exercise, to simplify $ 7y^2 + 5 - 9y^2 - 8 $, we combine the $ y^2 $ terms: $ 7y^2 $ and $ -9y^2 $.
This gives: \[ 7y^2 - 9y^2 = -2y^2. \]
Next, we combine the constants: \[ 5 - 8 = -3. \]
So, combining like terms helps you to simplify complex expressions into more manageable terms.

polynomial expressions

A polynomial expression is an algebraic expression that consists of variables and coefficients.
The variables can have whole number exponents (0, 1, 2, etc.).
In our exercise, $ 7y^2 + 5 - 9y^2 - 8 $ is a polynomial expression.
It includes two like terms with $ y^2 $ as the variable exponent and two constants (5 and -8).
Understanding the structure of polynomial expressions will make it easier to identify like terms and perform operations like combining them.

simplified expression

The end goal in simplifying algebraic expressions is to get a simplified expression.
This is an expression where all like terms are combined, and no further simplification is possible.
From our exercise, we started with $ 7y^2 + 5 - 9y^2 - 8 $.
After identifying and combining like terms, we ended up with $ -2y^2 - 3 $.
This is the simplified expression because there are no more like terms to combine and no further simplification can be done.
Simplified expressions are important because they provide the most concise form of the expression, making it easier to understand and use in further calculations.

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91影视

\(7 y^{2}+5-9 y^{2}-8\)

Short Answer

Step by step solution

Identify Like Terms

Combine Like Terms

Write the Simplified Expression

Key Concepts

like terms

combining like terms

polynomial expressions

simplified expression

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