Problem 9 Add or subtract as indicated. ... [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 9

Add or subtract as indicated. $$\left(-3 y^{2}+5 y-7\right)-\left(8 y^{3}+2 y^{2}+9 y\right)$$

Short Answer

Expert verified

-8y^3 - 5y^2 - 4y - 7

Step by step solution

- Distribute the Negative Sign

Rewrite the expression by distributing the negative sign to each term inside the parentheses: $-3y^2 + 5y - 7 - 8y^3 - 2y^2 - 9y$.

- Combine Like Terms

Group the like terms together:$-8y^3 + (-3y^2 - 2y^2) + (5y - 9y) - 7$.

- Simplify Each Group

Add or subtract the coefficients of each like term:$-8y^3 - 5y^2 - 4y - 7$.

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Key Concepts

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

Distributive Property

The distributive property helps us break down expressions and functions. In our exercise, we used this property when we distributed the negative sign across the second polynomial. Let's take a closer look at how it's applied:

Consider the expression $\text{{__(}}a \text{{__}} + b - ( c \text{{__}} - d )$
To simplify, distribute the negative sign to each term inside the parentheses: $\text{{__(}}a \text{{__}} + b - c + d$

In our exercise, we did this with $-3y^2 + 5y - 7 - (8y^3 + 2y^2 + 9y)$, distributing to get: $-3y^2 + 5y - 7 - 8y^3 - 2y^2 - 9y$. Remembering this simple step helps to avoid sign errors further in the problem-solving process.

Combining Like Terms

Combining like terms is crucial when working with polynomials. Terms are considered 'like' if they have the same variables and powers. In our step-by-step solution, we combined terms as follows:
$-8y^3 + (-3y^2 - 2y^2) + (5y - 9y) - 7$.

Key tips to remember:

Identify terms with the same variable and exponent.
Add or subtract the coefficients of these terms.

In our case, combining \-3y^2\ and \-2y^2\ gives \-5y^2\ and combining \5y\ and \-9y\ gives \-4y\.

Simplifying Expressions

Simplifying expressions involves making them as concise as possible. After distributing and combining like terms, our goal is to write the polynomial in its simplest form. Here are some steps to follow:

First, distribute any signs or multiply polynomials out if required.
Next, combine like terms to reduce the expression.
Finally, write the simplified expression in standard form, placing the terms in order of descending exponent.

Following these steps, our expression simplifies to: $-8y^3 - 5y^2 - 4y - 7$. This is the simplified version of the original problem, expressed neatly and ready to be interpreted.

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91影视

Add or subtract as indicated. $$\left(-3 y^{2}+5 y-7\right)-\left(8 y^{3}+2 y^{2}+9 y\right)$$

Short Answer

Step by step solution

- Distribute the Negative Sign

- Combine Like Terms

- Simplify Each Group

Key Concepts

Distributive Property

Combining Like Terms

Simplifying Expressions

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