Expressing algebraic expressions in standard form is a crucial skill in mathematics, particularly in simplifying and solving equations. The standard form of an algebraic expression typically involves expressing it in a way that groups like terms together, making it easier to work with. Here, we will simplify the expression "5x 15y 75" into standard form in five steps.
Understanding the Expression
The given expression is "5x 15y 75". This expression seems to lack clarity because it doesn't explicitly show the operations between the terms. However, based on the instructions, we will interpret this expression as 5x + 15y + 75.
Step 1: Combine Like Terms
The first step is to identify and combine like terms. In the expression 5x + 15y + 75, there are no like terms that can be combined because each term is unique.No Like Terms to Combine
- The term "5x" is unique and cannot be combined with "15y" or "75" because they are different variables and constants. - The term "15y" is also unique and cannot be combined with "5x" or "75". - The constant term "75" cannot be combined with "5x" or "15y".Step 2: Factor Out Common Factors
In this step, we look for common factors among the terms. However, in the expression 5x + 15y + 75, there are no common factors that can be factored out from all terms.No Common Factors to Factor Out
- There is no common variable or constant that can be factored out from "5x", "15y", and "75".Step 3: Simplify the Expression
Since we cannot combine like terms or factor out common factors, the expression remains as it is: 5x + 15y + 75. However, we can rearrange the terms to put the constant term last, following the standard form convention.Rearrange Terms
The rearranged expression is: 5x + 15y + 75. This is the simplest form of the expression given the instructions.Step 4: Consider Additional Simplifications
In some cases, additional simplifications might be possible, such as factoring or further rearranging terms for clarity. However, in this expression, no further simplifications are necessary or possible.Step 5: Finalize the Standard Form
Given that no further simplifications can be made and we have rearranged the terms for clarity, the final expression in standard form is 5x + 15y + 75.
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What is the standard form of an algebraic expression?
+The standard form of an algebraic expression typically involves expressing it in a way that groups like terms together, making it easier to work with.
How do I simplify an algebraic expression?
+To simplify an algebraic expression, combine like terms, factor out common factors, and rearrange terms for clarity.
What if I have trouble simplifying an expression?
+If you're having trouble simplifying an expression, try breaking it down into smaller parts, and look for common factors or like terms.