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\(x^4-16=\left(x^2\right)^2-4^2=\left(x^2-4\right)\left(x^2+4\right)=\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\)
\(x^2-64=x^2-8^2=\left(x-8\right)\left(x+8\right)\)
\(x^4-16=\left(x^2\right)^2-4^2=\left(x^2-4\right)\left(x^2+4\right)=\left(x-2\right)\left(x+2\right)\left(x^2+4\right)\\ x^2-64=x^2-8^2=\left(x-8\right)\left(x+8\right)\)
3. ( 22 + 1 ).( 24 + 1 ).( 28 + 1 )......( 264 + 1 ) + 1
= ( 22 - 1 ).( 22 + 1 ).( 24 + 1 ).( 28 + 1 )....( 264 + 1 ) + 1
= ( 24 - 1 ).( 24 + 1 ).( 28 + 1 )......( 264 + 1 ) + 1
= ( 28 + 1 ).....( 264 + 1 ) + 1
= ( 264 - 1 ).( 264 + 1 ) + 1
= 2128 - 1 + 1
= 2128
8.( 32 + 1 ).( 34 + 1 ).( 38 + 1 )....( 3128 + 1 ) + 1
= ( 32 - 1 ).( 32 + 1 ).( 34 + 1 ).( 38 + 1 )....( 3128 + 1 ) + 1
= ( 34 - 1 ).( 34 + 1 ).( 38 + 1 )....( 3128 + 1 ) + 1
= ( 38 - 1 ).( 38 + 1 )....( 3128 + 1 ) + 1
= ( 316 - 1 )......( 3128 + 1 ) + 1
= ( 3128 - 1 ).( 3128 + 1 ) + 1
= 3256 - 1 + 1
= 3256
\(\left(x-2\right)\left(x+2\right)\left(x^2+2^2\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)
\(=\left(x^2-2^2\right)\left(x^2+2^2\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)
\(=\left(x^4-2^4\right)\left(x^4+2^4\right)\left(x^8+2^8\right)-x^{16}\)
\(=\left(x^8-2^8\right)\left(x^8+2^8\right)-x^{16}\)
\(=\left(x^{16}-2^{16}\right)-x^{16}\)
\(=x^{16}-2^{16}-x^{16}\)
\(\left(-2\right)^{16}=65536\)