Use the distributive property to find the product of the given polynomials:
[tex]\begin{gathered} (3x-6)(2x^2-7x+1) \\ =(3x-6)(2x^2) \\ +(3x-6)(-7x) \\ +(3x-6)(1) \end{gathered}[/tex][tex]\begin{gathered} =(3x)(2x^2)+(-6)(2x^2) \\ +(3x)(-7x)+(-6)(-7x) \\ +(3x)(1)+(-6)(1) \end{gathered}[/tex][tex]\begin{gathered} =6x^3-12x^2 \\ -21x^2+42x \\ +3x-6 \end{gathered}[/tex]
Add like terms to simplify the sum:
[tex]\begin{gathered} =6x^3-12x^2-21x^2+42x+3x-6 \\ =6x^3-33x^2+45x-6 \end{gathered}[/tex]
Therefore:
[tex](3x-6)(2x^2-7x+1)=6x^3-33x+45x-6[/tex]
