Solution
David simplified a polynomial
[tex](4-x^2)(3x+2)+(5x^3-4x^2-7)[/tex]
For the first step
Open the brackets
[tex]\begin{gathered} (4-x^2)(3x+2)+(5x^3-4x^2-7) \\ =(12x+8-3x^3-2x^2)+(5x^3-4x^2-7) \end{gathered}[/tex]
The first step is correct.
For the second step
Collect like terms
[tex]\begin{gathered} (12x+8-3x^3-2x^2)+(5x^3-4x^2-7) \\ =(-3x^3+5x^3)+(-2x^2-4x^2)+(12x)+(8-7) \end{gathered}[/tex]
The second step is correct
For the third step
Add up the like terms
[tex]\begin{gathered} (-3x^3+5x^3)+(-2x^2-4x^2)+(12x)+(8-7) \\ =(2x^3)+(-6x^2)+(12x)+(1) \\ \text{Open the brackets} \\ =2x^3-6x^2+12x+1 \end{gathered}[/tex]
The third step is correct.
Hence, David did not make a mistake
