[tex]5a(a-3)-3a(a-5)=5a^2-15a-3a^2+15a=2a^2\\\\\\\frac{3x-6}{3}-5=x-2-5=x-7\\\\\\\frac{3a-9b}{3}-\frac{2a-4b}{2}=a-3b-(a-2b)=a-3b-a+2b=-b[/tex]
[tex]\\\\ \frac{2x+6}{2}-\frac{6x-9}{3}=x+3-(2x-3)=x+3-2x+3=-x+6\\\\\\\not{4}^2*\frac{x-7}{\not{2}^1}+\not{9}^3*\frac{x-1}{\not{3}^1}=2(x-7)+3(x-1)=2x-14+3x-3=5x-17[/tex]
[tex](x+7)(2x-1)=2x^2-x+14x-7=2x^2+13x-7\\\\\\(2a-1)(a+4)=2a^2+8a-a-4=2a^2+7a-4[/tex]
[tex](4a-1)(2-3a)=8a-12a^2-2+3a=-12a^2+11a-2\\\\\\(a^5-1)(a+1)-a^6=a^6+a^5-a-1=a^5-a-1[/tex]
[tex](2k^2-1)(2k+1)-4k^3=4k^3+2k^2-2k-1-4k^3= 2k^2-2k-1\\\\\\(3p^2-p)(3-p)=9p^2-3p^3-3p+p^2=-3p^3+10p^2-3p[/tex]
[tex](a-b)(a^2+ab+b^2)= a^3+a^2b+ab^2 - a^2b-ab^2-b^3=a^3-b^3\\\\\\(a+b)(a^2-ab+b^2) =a^3-a^2b+ab^2+a^2b-ab^2+b^3 =a^3+b^3[/tex]
