Problem 12 Simplify. $$8 y-6 y$$... [FREE SOLUTION]

Chapter 4: Problem 12

Simplify. $$8 y-6 y$$

Short Answer

Expert verified

So, the simplified form of the expression $8y - 6y$ is $2y$.

Step by step solution

Identifying like terms

In the expression $8y - 6y$, the like terms are $8y$ and $-6y$. These terms can be combined because they have the same variable $y$.

Combining like terms

To simplify the expression, simply subtract the coefficients (the numbers in front of the variable). This is done as follows: $8y - 6y = 2y$.

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Key Concepts

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

Understanding Like Terms

When working with algebraic expressions, it's essential to identify like terms. Like terms are terms that have exactly the same variables raised to the same power. This uniformity means that in order to be considered like terms, they must match perfectly in variable and exponent. For example, in the expression $8y - 6y$, both terms have the variable $y$ and are thus like terms.

Identifying like terms is the first step towards simplifying an algebraic expression because only like terms can be combined through addition or subtraction. It's much like combining apples with apples, meaning you wouldn't add apples to oranges鈥攖hey're simply not the same!

How to Combine Like Terms

Combining like terms is a fundamental process in simplifying algebraic expressions. After identifying the like terms鈥攐r terms that share the same variables鈥攜ou can combine them to make the expression simpler. This process involves adjusting the coefficients (the numbers in front of the variables).

To combine like terms, focus solely on the coefficients. The variable part remains unchanged.
In the expression $8y - 6y$, you're looking at the numbers 8 and -6.
Subtract the coefficients, like you would with simple arithmetic: $8 - 6$.
This gives you 2. So, $8y - 6y$ simplifies to $2y$.

Remember, the key is to perform the operation using the numerical coefficients while keeping the common variable factor intact. This way, you effectively and accurately combine like terms.

Coefficients Explained

Coefficients are a fundamental component of algebraic terms that help express the quantity of the variable involved. In any given algebraic term, the coefficient is the numerical part that comes before the variable.

In the expression $8y - 6y$, 8 and -6 are the coefficients. These numbers give context to how many times the variable is being considered within a term:

An algebraic term like $8y$ denotes that the variable $y$ is multiplied by 8.
Similarly, the term $-6y$ signals that $y$ is multiplied by -6.

Understanding coefficients is crucial because they determine how terms are combined and simplified. When you subtract or add algebraic terms, focus on combining these coefficients since they tell you the precise "amount" of each variable present in the expression.

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91影视

Simplify. $$8 y-6 y$$

Short Answer

Step by step solution

Identifying like terms

Combining like terms

Key Concepts

Understanding Like Terms

How to Combine Like Terms

Coefficients Explained

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