To determine the equivalent expressions, we first need to simplify the given polynomial expression. Let's break down what has been provided.
The expression is:
\( 6(5x - 4) - (3x * 2 - (4xy + (2x) * (x + 4y))) \)
Let's simplify it step by step:
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Distribute \( 6 \) in the first term: \[ 6(5x) - 6(4) = 30x - 24 \]
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Simplify the second term. Start with the expression inside the parentheses: \[ 3x * 2 = 6x \] Thus, we now have: \[ 6x - (4xy + (2x)(x + 4y)) \]
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Next, simplify \( (2x)(x + 4y) \): \[ 2x * x + 2x * 4y = 2x^2 + 8xy \] So the expression becomes: \[ 6x - (4xy + 2x^2 + 8xy) \] Combine like terms inside the parentheses: \[ 4xy + 8xy = 12xy \] Thus, we now have: \[ 6x - (2x^2 + 12xy) \]
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Distribute the negative sign: \[ 6x - 2x^2 - 12xy \]
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Now, combine everything: \[ 30x - 24 - 6x + 2x^2 + 12xy \] Combine like terms: \[ 30x - 6x = 24x \] Hence, we have: \[ -2x^2 + 24x - 12xy - 24 \]
If you have specific expressions to compare this result to, please provide them. We will check if they are equivalent by complying with the steps of grouping and simplifying each.
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