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Chapter 4: Problem 44

Simplify. $$ (-6 x+8 y)+(6 x+2 y) $$

Short Answer

Expert verified
10y

Step by step solution

01

Identify Like Terms

Recognize the like terms in the expression. The given expression is ewlineewline(-6x + 8y) + (6x + 2y)ewlineewlineHere, -6x and 6x are like terms, and 8y and 2y are like terms.
02

Combine Like Terms

Add the like terms separately. First, combine the x-terms:ewline(-6x + 6x) = 0xewlineewlineNext, combine the y-terms:ewline(8y + 2y) = 10y
03

Simplify the Expression

Now combine the simplified terms from Step 2. Since 0x is zero, it does not need to be included in the final expression. The simplified expression is:ewline10y

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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 variables raised to the same power. This makes them easily combinable. For example, in the expression (-6x + 8y) + (6x + 2y), the like terms are:
  • -6x and 6x
  • 8y and 2y
Recognizing like terms is crucial for simplifying algebraic expressions. Each term must have the same variable components. For instance,
  • 3x and -2x are like terms
  • 5y and y are like terms (with an implicit '1' as the coefficient)
  • 4x^2 and -x^2 are like terms
Practicing to identify like terms will make solving algebraic problems much easier!
combining like terms
Once you have identified the like terms, the next step is to combine them. Combining like terms involves adding or subtracting their coefficients. For example, in the expression: (-6x + 8y) + (6x + 2y)
We can combine:
  • -6x and 6x to get 0x
  • 8y and 2y to get 10y
Combining like terms simplifies the expression, making it easier to work with and understand. Here's a pro tip:
  • Always perform addition or subtraction of coefficients step by step.
  • Double-check to confirm that the terms being combined are indeed like terms.
  • Keep the variable part unchanged during this process.
Identifying and combining like terms accurately will ensure correct results.
simplifying expressions
Simplifying expressions means making them as clear and concise as possible. After identifying and combining like terms, simplifying the expression is the final step. For the given exercise:
The original expression is: (-6x + 8y) + (6x + 2y)
Step-by-step simplification:
  • Identify like terms: -6x and 6x, 8y and 2y
  • Combine the x-terms: -6x + 6x = 0x
  • Combine the y-terms: 8y + 2y = 10y
After combining, we get: 0x + 10y
Since 0x equals zero, it can be omitted from the expression.
Hence, the simplified expression is 10y.
Simplifying expressions helps eliminate unnecessary components, making further calculations easier. Always remember:
  • Perform operations carefully step-by-step.
  • Eliminate zero coefficients to simplify the final answer.
Practice simplifying different expressions to gain confidence and efficiency in solving algebraic equations.

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