Let's go through the steps Sharina took to simplify the expression [tex]\(3(2x-6-x+1)^2 - 2 + 4x\)[/tex]:
1. Simplifying within the parentheses:
The original expression is [tex]\(3(2x-6-x+1)^2 - 2 + 4x\)[/tex].
Within the parentheses:
[tex]\[
2x - 6 - x + 1 = x - 5
\][/tex]
This gives us:
[tex]\[
3(x-5)^2 - 2 + 4x
\][/tex]
So, Step 1 is correct: [tex]\(3(x-5)^2 - 2 + 4x\)[/tex].
2. Expanding the exponent:
Next, we expand [tex]\((x-5)^2\)[/tex]:
[tex]\[
(x-5)^2 = x^2 - 10x + 25
\][/tex]
Plugging this back into the expression, we get:
[tex]\[
3(x^2 - 10x + 25) - 2 + 4x
\][/tex]
So, Step 2 is correct: [tex]\(3(x^2 - 10x + 25) - 2 + 4x\)[/tex].
3. Distributing the 3 to each term in the parentheses:
Now, we distribute 3 to each term inside the parentheses:
[tex]\[
3 \cdot x^2 = 3x^2
\][/tex]
[tex]\[
3 \cdot (-10x) = -30x
\][/tex]
[tex]\[
3 \cdot 25 = 75
\][/tex]
This results in:
[tex]\[
3x^2 - 30x + 75 - 2 + 4x
\][/tex]
So, Step 3 should be: [tex]\(3x^2 - 30x + 75 - 2 + 4x\)[/tex].
4. Combining like terms to get the final simplified expression:
Now, we need to combine like terms:
Combine the [tex]\(x\)[/tex]-terms:
[tex]\[
-30x + 4x = -26x
\][/tex]
Combine the constants:
[tex]\[
75 - 2 = 73
\][/tex]
This results in the final simplified expression:
[tex]\[
3x^2 - 26x + 73
\][/tex]
So, a possible next step in Sharina's work would be Distribute the 3 to each term in the parentheses by multiplying.
