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Kristen wants to simplify the following expression so that she doesn't have to do as much math every time she uses it.
[tex]\[ 3(-5x + 5y) + 3(-x - 4y) - 2(5x - 5y) \][/tex]

What is the simplest way to write the expression?

A. [tex]\(-8x - 7y\)[/tex]
B. [tex]\(8x + 17y\)[/tex]
C. [tex]\(28x + 37y\)[/tex]
D. [tex]\(-28x + 13y\)[/tex]



Answer :

GinnyAnswer
Certainly! Let's go through the process of simplifying the given expression step by step.

The expression provided is:
[tex]\[ 3(-5x + 5y) + 3(-x - 4y) - 2(5x - 5y) \][/tex]

First, let's distribute the constants (3 and -2) through their respective parentheses:

1. Distribute the 3 in the first term:
[tex]\[ 3(-5x + 5y) = 3 \cdot (-5x) + 3 \cdot (5y) = -15x + 15y \][/tex]

2. Distribute the 3 in the second term:
[tex]\[ 3(-x - 4y) = 3 \cdot (-x) + 3 \cdot (-4y) = -3x - 12y \][/tex]

3. Distribute the -2 in the third term:
[tex]\[ -2(5x - 5y) = -2 \cdot (5x) - 2 \cdot (-5y) = -10x + 10y \][/tex]

Next, combine all the expressions:
[tex]\[ -15x + 15y + (-3x - 12y) + (-10x + 10y) \][/tex]

Now, group the like terms together:

Combine the [tex]\(x\)[/tex]-terms:
[tex]\[ -15x - 3x - 10x = -28x \][/tex]

Combine the [tex]\(y\)[/tex]-terms:
[tex]\[ 15y - 12y + 10y = 13y \][/tex]

So the simplified expression is:
[tex]\[ -28x + 13y \][/tex]

Therefore, the simplest form of the expression [tex]\(3(-5x + 5y) + 3(-x - 4y) - 2(5x - 5y)\)[/tex] is:

[tex]\[ \boxed{-28x + 13y} \][/tex]

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