Problem 3 Simplify each of the following p... [FREE SOLUTION]

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Painless Algebra

Lynette Long

$Math Studyset 91影视 Explanations$ Math

2 Edition

Chapter 7: Problem 3

Simplify each of the following problems by adding or subtracting. $$ 3 x^{2}-5 x^{2} $$

Short Answer

Expert verified

-2x^2

Step by step solution

Identify Like Terms

Recognize that both terms, $3x^2$ and $-5x^2$, are like terms because they both contain $x^2$.

Combine the Coefficients

Since these terms are like terms, combine their coefficients: $3$ and $-5$.

Perform the Arithmetic Operation

Subtract the coefficients: $3 - 5 = -2$.

Write the Simplified Expression

The simplified expression is $-2x^2$.

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Key Concepts

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

like terms

In algebra, 'like terms' are terms that have the same variable raised to the same power. For example, in the expression $3x^2 - 5x^2$, both terms have the variable $x$ raised to the power of 2. This makes $3x^2$ and $-5x^2$ 'like terms'. When simplifying expressions, it's crucial to identify like terms so you know which terms you can combine. Always look for the same variable with the same exponent. If the variables or their exponents differ, the terms are not like terms and cannot be combined directly.

coefficients

Coefficients are the numerical parts of terms that multiply the variables. In the expression $3x^2 - 5x^2$, the numbers $3$ and $-5$ are the coefficients, while $x^2$ is the variable part. When combining like terms, you keep the variable part the same and simply add or subtract the coefficients.

For example:

In $3x^2$, the coefficient is 3.
In $-5x^2$, the coefficient is $-5$.

Being able to identify and work with coefficients is essential for simplifying expressions.

arithmetic operations

Arithmetic operations are basic math calculations like addition, subtraction, multiplication, and division. When simplifying expressions involving like terms, usually addition and subtraction of coefficients are the primary operations.

In the problem $3x^2 - 5x^2$, we perform subtraction because the second term is subtracted from the first. We only perform this subtraction on the coefficients:$3 - 5 = -2$. The variable part $x^2$ remains the same.

simplified expression

A simplified expression is an expression where all like terms have been combined, and it is easier to understand and solve. Returning to our example:

After recognizing like terms and combining the coefficients ($3 - 5 = -2$), we get the simplified expression $-2x^2$. The final result, $-2x^2$, has fewer terms and is more straightforward. Simplifying makes it easier to see and understand the relationships between different terms in an expression.

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91影视

Simplify each of the following problems by adding or subtracting. $$ 3 x^{2}-5 x^{2} $$

Short Answer

Step by step solution

Identify Like Terms

Combine the Coefficients

Perform the Arithmetic Operation

Write the Simplified Expression

Key Concepts

like terms

coefficients

arithmetic operations

simplified expression

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