Which expression is equivalent to

General
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which expression is equivalent to

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Which expression is equivalent to

Answer:
It’s important to note that the specific expression we need to analyze is missing from your question. However, I can guide you through a typical procedure for finding an equivalent expression in algebra.

Step-by-Step Guide to Finding Equivalent Expressions

  1. Identify Like Terms:

    • Like terms are terms that have the same variable raised to the same power. Example: (3x) and (5x) are like terms, whereas (3x) and (3x^2) are not.

  2. Combine Like Terms:

    • Add or subtract coefficients of like terms. Example: (6x + 2x = 8x).

  3. Factor Common Factors:

    • Look for common factors in each term. Example: (4x + 6y) has a common factor of 2, so it can be factored as (2(2x + 3y)).

  4. Use Distributive Property:

    • Expand expressions using the distributive property (a(b + c) = ab + ac). Example: (3(2x + 4) = 6x + 12).

  5. Simplify Fractions:

    • Simplify any fractions if possible. Example: (\frac{4x}{2} = 2x).

Let’s go through an example problem to illustrate these steps:

Example Problem

Given Expression:
[ 2(3x + 4y) - x + 5(2y - 3) ]

Solution:

  1. Distribute the Constants:

    • First, apply the distributive property to (2(3x + 4y)) and (5(2y - 3)):

      2(3x) + 2(4y) = 6x + 8y
      5(2y) + 5(-3) = 10y - 15

    • The expression now becomes:

      6x + 8y - x + 10y - 15

  2. Combine Like Terms:

    • Combine the (x) terms: (6x - x = 5x)

    • Combine the (y) terms: (8y + 10y = 18y)

    • The simplified expression is:

      5x + 18y - 15

  3. Factor Out Common Factors (if necessary):

    • In this case, no further factoring is needed as the terms do not share a common factor beyond one.

Final Answer:
[ 5x + 18y - 15 ]

This is the equivalent expression for the given algebraic expression.

If you provide the specific expression you need to work on, I can give a more tailored and precise solution to find its equivalent expression!