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use the binomial theorem to expand and simplify (y^2-2)^6 )(y^2+2)^6

( a - b ) * ( a + b ) = a ^ 2 - b ^ 2

( y ^ 2 - 2 ) * ( y ^ 2 + 2 ) =

( y ^ 2 ) ^ 2 - ( 2 ^ 2 ) ^ 2 =

y ^ 4 - 4

( y ^ 2 - 2 ) ^ 6 * ( y ^ 2 + 2 ) ^ 6 =

[ ( y ^ 2 - 2 ) * ( y ^ 2 + 2 ) ] ^ 6 =

( y ^ 4 - 4 ) ^ 6

( a - b ) ^ 6 =

a^6-6 a^5 b+15 a^4 b^2-20 a^3 b^3+15 a^2 b^4-6 a b^5+b^6

( y ^ 4 - 4 ) ^ 6 =

( y ^ 4 ) ^ 6 - 6 * ( y ^ 4 ) ^ 5 * 4 + 15 * ( y ^ 4 ) ^ 4 * 4 ^ 2 -
20 * ( y ^ 4 ) ^ 3 * 4 ^ 3 + 15 *( y ^ 4 ) ^ 2 * 4 ^ 4 - 6 * ( y ^ 4 ) * 4 ^ 5 + 4 ^ 6 =

y ^ 24 - 6 * y ^ 20 * 4 + 15 * y ^ 16 * 16 - 20 y ^ 12 * 64 + 15 y ^ 8 * 256
- 6 * y ^ 4 * 1024 + 4096 =

y ^ 24 - 24 y ^ 20 + 240 y ^ 16 - 1280 y ^ 12 + 3840 y ^ 8 - 6144 y ^ 4 + 4096

( y ^ 2 - 2 ) ^ 6 * ( y ^ 2 + 2 ) ^ 6 =

( y ^ 4 - 4 ) ^ 6 =

y ^ 24 - 24 y ^ 20 + 240 y ^ 16 - 1280 y ^ 12 + 3840 y ^ 8 - 6144 y ^ 4 + 4096

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