Problem 80 Simplify by combining like terms... [FREE SOLUTION]

Chapter 3: Problem 80

Simplify by combining like terms. $$-j^{3}-j^{3}$$

Short Answer

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Question: Simplify the expression $$-j^{3}-j^{3}$$. Answer: $$-2j^{3}$$

Step by step solution

Identify the like terms

Notice that both terms in the expression are like terms since they have the same power 3 of the variable j: $$-j^{3}$$ and $$-j^{3}$$.

Combine the coefficients of the like terms

To combine like terms, add their coefficients: since the coefficients of both terms are -1, we have $$-1 - 1 = -2$$.

Write the simplified expression

Now, we can write the simplified expression by multiplying the combined coefficient with the common variable and its power: $$-2j^{3}$$. The simplified expression is $$-2j^{3}$$.

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Key Concepts

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

Simplifying Algebraic Expressions

Simplifying algebraic expressions is like finding the shortest path to reach a destination in a maze.
You start by grouping terms that can be combined, known as like terms. This process helps make expressions more manageable and easier to work with.

Here's how it works:

Identify terms with the same variable and exponent. These are your like terms. In our example, $-j^3$ and $-j^3$ are like terms because they both have $j^3$.
Once identified, combine these like terms by adding or subtracting their coefficients. This process is what we call simplifying.
Finally, rewrite the expression with the simplified terms.

The key is to focus on gathering similar pieces, much like sorting socks from your laundry.

Coefficients in Algebra

In algebra, coefficients play the role of the numbers in charge.
They tell you how many of each variable you have. Understanding coefficients is crucial because they determine the scale of each term within an expression.

Consider this:

Coefficients are the numbers directly in front of variables. In $-j^3$, the coefficient is $-1$.
When combining like terms, add or subtract their coefficients. For $-j^3 - j^3$, you calculate $-1 - 1 = -2$.
This combined coefficient is then multiplied by the variable and its power, completing the simplified expression.

Coefficients provide a sense of scale and quantity to variables, acting as their numerical guides.

Polynomials

Polynomials are like the multi-storied buildings of algebra.
They're made up of terms, each consisting of a coefficient, a variable, and an exponent.

Understanding polynomials involves:

Recognizing each term within the polynomial structure. These terms could be constants, variables, or a mix of both.
Identifying like terms within the polynomial to simplify it effectively. In our example, $-j^3$ and $-j^3$ are not just terms but parts of a polynomial.
Combining these like terms to streamline the polynomial and make calculations more straightforward.

Polynomials form the backbone of many algebraic operations, and mastering them is key to proficiency in algebra.

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91影视

Simplify by combining like terms. $$-j^{3}-j^{3}$$

Short Answer

Step by step solution

Identify the like terms

Combine the coefficients of the like terms

Write the simplified expression

Key Concepts

Simplifying Algebraic Expressions

Coefficients in Algebra

Polynomials

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