3x(3x+7)-(3x+1)^2=9x^2+21x-(9x^2-6x+1)=9x^2+21x-9x^2+6x-1=27x-1
(y-2)(y+3)-(y-1)^2=y^2+3y-2y-6-(y^2-2y+1)=y^2+y-6-y^2+2y-1=3y-1
(p+1)^2-(p+2)^2=p^2+2p+1-(p^2-4p+4)=p^2+2p+1-p^2+4p-4=6p-4
4(a+5)^2-(4a^2+40a)=4(a^2+10a+25)-4a^2-40a=4a^2+40a+100-4a^2-40a=100
4b(3b+6)-(3b-5)(3b+5)=12b^2+24b-(9b^2+15b-15b-25)=12b^2+24b-9b^2+25=3b^2+24B+25
(C-5)(c-1)-(c-6)^2=c^2-c-5c+5-(c^2-12c+36)=c^2-6c+5-c^2+12c-36=6c-31
(y-4)^2-(4-y)(4+y)=y^2-8y+16-(16+4y-4y-y^2)=y^2-8y+16-16+y^2=2y^2-8y
(4ab-b^2)+2(a-b)^2=4ab-b^2+2(a^2-2ab+b^2)=4ab-b^2+2a^2-4ab+2b^2=b^2+2A^2