Questions: You were asked to simplify the following algebraic expression: -2(3x+4)-(4y+2) Next, using the commutative property of addition, group the like terms. Do not combine any like terms yet. -6x-8-4y-2=

You were asked to simplify the following algebraic expression:
-2(3x+4)-(4y+2)

Next, using the commutative property of addition, group the like terms. Do not combine any like terms yet.
-6x-8-4y-2=

Transcript text: learn.hawkeslearning.com/Portal/Lesson/lesson_practice:I! O Back to Practice Lesson: 2.1b Simplifying Expressions Question 4 of 10 , Step 1 of 1 $3 / 10$ Correct Tutor Explain Error Step By Step Step By Step 2 of 3 You were asked to simplify the following algebraic expression: \[ -2(3 x+4)-(4 y+2) \] Next, using the commutative property of addition, group the like terms. Do not combine any like terms yet. \[ -6 x-8-4 y-2= \] $\square$ Back to Practice Previous Page Next Page Display Step Answer O 2024 Hawkes Learning

Solution

Solution Steps

To simplify the given algebraic expression, we need to distribute the multiplication over addition and then group the like terms. The expression is $-2(3x + 4) - (4y + 2)$. First, distribute $-2$ across $(3x + 4)$ and $-1$ across $(4y + 2)$. Then, group the like terms together.

Step 1: Distribute the Multiplication

To simplify the expression $-2(3x + 4) - (4y + 2)$, we first distribute the multiplication over addition. This involves multiplying $-2$ by each term inside the first parentheses and $-1$ by each term inside the second parentheses:

\[ -2(3x + 4) = -6x - 8 \]

\[ -(4y + 2) = -4y - 2 \]

Step 2: Combine the Results

Next, we combine the results from the distribution:

\[ -6x - 8 - 4y - 2 \]

Step 3: Group Like Terms

Now, we group the like terms together. The terms involving $x$ and $y$ are already grouped, and the constant terms can be combined:

\[ -6x - 4y - (8 + 2) \]

Step 4: Simplify the Expression

Finally, we simplify the expression by combining the constant terms:

\[ -6x - 4y - 10 \]