Answer:
Options 1, 3, and 4.
Explanation:
Given the expression:
[tex]3x\mleft(x-12x\mright)+3x^2-2\mleft(x-2\mright)^2[/tex]
Step 1: The term -2(x-2)² is simplified by first squaring the expression x-2.
[tex]\begin{gathered} 3x(x-12x)+3x^2-2(x-2)^2 \\ =3x(x-12x)+3x^2-2(x-2)(x-2) \\ =3x(x-12x)+3x^2-2(x^2-2x-2x+4) \\ =3x(x-12x)+3x^2-2(x^2-4x+4) \end{gathered}[/tex]
Step 2: The parentheses are eliminated through multiplication.
[tex]=3x^2-36x^2+3x^2-2x^2+8x-8[/tex]
Step 3: After multiplying, the like terms are combined by adding and subtracting.
[tex]\begin{gathered} =3x^2-36x^2+3x^2-2x^2+8x-8 \\ =-32x^2+8x-8 \end{gathered}[/tex]
The three options that are correct are Options 1, 3, and 4.
