a)
\(x^4+4=(x^2)^2+2^2+2.x^2.2-4x^2\)
\(=(x^2+2)^2-(2x)^2=(x^2+2-2x)(x^2+2+2x)\)
b)
\(64x^4+81=(8x^2)^2+9^2+2.8x^2.9-144x^2\)
\(=(8x^2+9)^2-(12x)^2=(8x^2+9-12x)(8x^2+9+12x)\)
c)
\(x^8+4=(x^4)^2+2^2+2.x^4.2-4x^4\)
\(=(x^4+2)^2-(2x^2)^2=(x^4+2-2x^2)(x^4+2+2x^2)\)
d)
\(x^4+18x^2=(x^2)^2+18^2+2.x^2.18-36x^2\)
\(=(x^2+18)^2-(6x)^2=(x^2+18-6x)(x^2+18+6x)\)
e)
\(x^4+3x^2+4=(x^2)^2+2^2+2.x^2.2-x^2\)
\(=(x^2+2)^2-x^2=(x^2+2-x)(x^2+2+x)\)
f)
\(x^4-7x^2+1=(x^4-2x^2+1)-9x^2\)
\(=(x^2-1)^2-(3x)^2=(x^2-1-3x)(x^2-1+3x)\)