Question:
[tex](3x^2-5x+7)(2x^2+x-2)[/tex]
Step 1: Apply the distributive law
[tex]\begin{gathered} (a+b)(x+y+z)=a(x+y+z)+b(x+y+z) \\ =ax+ay+az+bx+by+bz \end{gathered}[/tex]
Step 2: Apply the foil method of multiplication
[tex]\begin{gathered} (3x^2-5x+7)(2x^2+x-2) \\ =3x^2(2x^2+x-2)-5x(2x^2+x-2)+7(2x^2+x-2) \end{gathered}[/tex]
Step 3: Expand the brackets
[tex]\begin{gathered} 3x^2(2x^2+x-2)-5x(2x^2+x-2)+7(2x^2+x-2) \\ 6x^4+3x^3-6x^2-10x^3-5x^2+10x+14x^2+7x-14 \\ \text{note: take note of the signs when expanding the brackets} \end{gathered}[/tex]
Step 4: Collect similar terms
[tex]\begin{gathered} 6x^4+3x^3-6x^2-10x^3-5x^2+10x+14x^2+7x-14 \\ =6x^4+3x^3-10x^3-6x^2-5x^2+14x^2+10x+7x-14 \\ =6x^4-7x^3+3x^2+17x-14 \end{gathered}[/tex]
Therefore,
The final answer is = 6x⁴ - 7x³ + 3x² + 17x - 14
