[tex]a)\\3a^2+2a(3a-1)-3(4a-3)+2a=3a^2+6a^2-2a-12a+9+2a=9a^2-12a+9\\\\9*(-\frac23)^2-12*(-\frac23)-12=9*\frac49+4*2-12=4+8-12=12-12=0[/tex]
[tex]b)\\(5p-1)(p-2)+\frac13(6-6p^2-3p)=5p^2-10p-p+2+2-2p^2-p=3p^2-12p+4\\\\3*2^2-12*2+4=3*4-24+4=12-24+4=-12+4=-8[/tex]
[tex]c)\\2.5b(2b-1)+(1-3b)(1-3b)=5b^2-2.5b+(1-3b)^2=5b^2-2.5b+1-6b+9b^2=14b^2-8.5b+1\\\\14*(-1)^2-8.5*1+1=14-8.5+1=15-8.5=6.5[/tex]
[tex]d)\\7a(2a-3)+4(6a-3a^2)=14a^2-21a+24a-12a^2=2a^2+3a\\\\2*(\frac12\sqrt3)^2+3*\frac12\sqrt3=2*\frac34+\frac32\sqrt3=\frac32+\frac32\sqrt3=\frac{3+3\sqrt3}2[/tex]
[tex]e)\\5(2p-3r)-4(-3p+r)-(6p+7r)=10p-15r+12p-4r-6p-7r=16p-26r\\\\16*(-3)-26*2=-48-52=-100[/tex]
[tex]f)\\-(a+1)(2b-3)+6(a+\frac13b)=-(2ab-3a+2b-3)+6a+2b=-2ab+3a-2b+3+6a+2b=-2ab+9a+3\\\\-2*5*2+9*5+3=-20+45+3=-20+48=28[/tex]
[tex]g)\\(3s-4t)(2t+s)+(s+1)(3t+1)=6ts+3s^2-8t^2-4ts+3ts+s+3t+1=5ts+3s^2-8t^2+s+3t+1\\\\5*1*\sqrt2+3*(\sqrt2)^2-8*1^2+\sqrt2+3*1+1=5\sqrt2+6-8+\sqrt2+3+1=6\sqrt2+2[/tex]
