We want to simplify the following expression
[tex](2x-3)(5x^4-7x^3+6x^2-9)[/tex]
To simplify this expression, we just need to use the distributive property of multiplication.
[tex](a+b)(c+d)=ac+ad+bc+bd[/tex]
Using this property in our expression, we have
[tex]\begin{gathered} (2x-3)(5x^4-7x^3+6x^2-9) \\ =2x\cdot5x^4-2x\cdot7x^3+2x\cdot6x^2+2x\cdot(-9)-3\cdot5x^4-3\cdot(-7x^3)-3\cdot6x^2-3\cdot(-9) \\ =10x^5-14x^4+12x^3-18x-15x^4+21x^3-18x^2+27 \\ =10x^5-29x^4+33x^3-18x^2-18x+27 \end{gathered}[/tex]
