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(1+3x)²-(1-3x²) = 1+6x+9x²-1+3x² = 12x²+6x
b)
(1-2x²)²-(2-x²)²=1-4x²+4x⁴-(4-4x²+x⁴)=1-4x²+4x⁴-4+4x²-x⁴=3x⁴-3
c)
(√5-3x²)(√5+3x²)+(1+3x²)² = 5-9x⁴+1+6x²+9x⁴ = 6x²+6
d)
(√2/2x²+1)(√2/2x²-1)-1/2(x²+x)² = 1/2x⁴-1-1/2(x⁴+2x³+x²)=
1/2x⁴-1-1/2x⁴-x³-1/2x² = -x³-1/2x²-1