`1)`
`A=2x^{2}(3x+4)(3x-4)-9/2 (2x^2+1).(2x^2-1)`
`=2x^{2}.[(3x)^2-4^2]-9/2 .[(2x^2)^2-1]`
`=2x^2 .(9x^2-16)-9/2 .(4x^4-1)`
`=18x^4-32x^2-18x^4+9/2`
`=-32x^2+9/2`
`3)`
`C=2x(2x-1)^2-3x(x+3).(x-3)-4x(x+1)^2`
`=2x.[(2x)^2-4x+1]-3x.(x^2-3^2)-4x(x^2+2x+1)`
`=2x.(4x^2-4x+1)-3x(x^2-9)-4x^3-8x^2-4x`
`=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x`
`=(8x^3-7x^3-4x^3)+(-8x^2-8x^2)+(2x+27x-4x)`
`=x^3-16x^2+25x`
`5)`
`E=(2x-1).(4x^2+2x+1)-2x(2x-7)(2x+7)`
`=(2x)^3-1-2x.[(2x)^2-7^2]`
`=8x^3-1-2x.(4x^2-49)`
`=8x^3-1-8x^3+98x`
`=-1+98x`
`7)`
`G=(x+1)^3+(x-1)^3+x^3-3x(x+1).(x-1)`
`=(x+1+x-1).[(x+1)^2-(x+1).(x-1)+(x-1)^2]+x^3-3x(x^2-1)`
`=2x.(x^2+2x+1-x^2+1+x^2-2x+1)+x^3-3x^3+3x`
`=2x.(x^2+3)+x^3-3x^3+3x`
`=2x^3+6x+x^3-3x^3+3x`
`=9x`
`9)`
`K=(a+b+c)^2+(a+b-c)^2+(2a-b)^2`
`=[(a+b)+c]^2+[(a+b)-c]^2+(2a-b)^2`
`=(a+b)^2+2(a+b).c+c^2+(a+b)^2-2(a+b).c+c^2+(2a-b)^2`
`=2(a+b)^2+2c^2+(2a-b)^2`
`=2.(a^2+2ab+b^2)+2c^2+(4a^2-4ab+b^2)`
`=2a^2+4ab+2b^2+2c^2+4a^2-4ab+b^2`
`=6a^2+3b^2+2c^2`
