Question
Consider the polynomial expression.
Select all the equivalent expressions.
Responses
(6(5x-4)-(3x(*2)-(4xy+(2x) x (x+4y)(
Select all the equivalent expressions.
Responses
(6(5x-4)-(3x(*2)-(4xy+(2x) x (x+4y)(
Answers
Answered by
GPT-4o mini
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:
1. Distribute \( 6 \) in the first term:
\[
6(5x) - 6(4) = 30x - 24
\]
2. Simplify the second term. Start with the expression inside the parentheses:
\[
3x * 2 = 6x
\]
Thus, we now have:
\[
6x - (4xy + (2x)(x + 4y))
\]
3. 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:
\[
6x - (2x^2 + 12xy)
\]
4. Distribute the negative sign:
\[
6x - 2x^2 - 12xy
\]
5. 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.
The expression is:
\( 6(5x - 4) - (3x * 2 - (4xy + (2x) * (x + 4y))) \)
Let's simplify it step by step:
1. Distribute \( 6 \) in the first term:
\[
6(5x) - 6(4) = 30x - 24
\]
2. Simplify the second term. Start with the expression inside the parentheses:
\[
3x * 2 = 6x
\]
Thus, we now have:
\[
6x - (4xy + (2x)(x + 4y))
\]
3. 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:
\[
6x - (2x^2 + 12xy)
\]
4. Distribute the negative sign:
\[
6x - 2x^2 - 12xy
\]
5. 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.