\(a=x^4+4=x^4+4+4x^2-4x^2=\left(x^2+2\right)^2-4x^2=\left(x^2+2+2x\right)\left(x^2+2-2x\right)\)
\(b=4x^4+81=4x^4+81+36x^2-36x^2=\left(2x^2+9\right)^2-36x^2=\left(2x^2+9+6x\right)\left(2x^2+9-6x\right)\)
\(c=x^4+64y^4=x^4+64y^4+\left(16xy\right)^2-\left(16xy\right)^2=\left(x^2+8y^2\right)^2-\left(16xy\right)^2=\left(x^2+8y^2+4xy\right)\left(x^2+8y^2-4xy\right)\)
\(d=x^4y^4+4=x^4y^4+4+\left(4xy\right)^2-\left(4xy^2\right)=\left(x^2y^2+2\right)^2-\left(4xy\right)^2=\left(x^2y^2+2+2xy\right)\left(x^2+2-2xy\right)\)
a) \(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
b) \(4x^4+81\)
\(=4x^4+81+36x^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
c) \(x^4+64y^4\)
\(=x^4+64y^4+16x^2y^2-16x^2y^2\)
\(=\left(8y^2+x^2\right)^2-\left(4xy\right)^2\)
\(=\left(8y^2+x^2-4xy\right)\left(8y^2+x^2+4xy\right)\)
d) \(x^4y^4+4\)
\(=x^4y^4+4+4xy^2-4xy^2\)
\(=\left(x^2y^2+2\right)^2-\left(4xy\right)^2\)
\(=\left(x^2y^2+2-2xy\right)\left(x^2y^2+2+2xy\right)\)
a)x4+4
=x4+4x2+4-4x2
=(x4+4x2+4)-4x2
=(x2+2)2-4x2
=(x2+2-2x)(x2+2+2x)
x4+81
=x4+36x2+81-36x2
=(x4+36x2+81)-36x2
=(x2+9)2-36x2
=(x2+9-6x)(x2+9+6x)
