Question

Answer 1

\(x^4+4=x^4+4+4x^2-4x^2=\left(x^4+4x^2+4\right)-\left(2x\right)^2=\left(x^2+2\right)^2-\left(2x^2\right)=\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)

\(4x^4+1 =(2x^2)^2+4x^2+1-4x^2 =(2x^2+1)^2-(2x)^2 =(2x^2+1+2x)(2x^2+1-2x)\)

Answer 2

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: \(4x^4+1\)

\(=4x^4+4x^2+1-4x^2\)

\(=\left(2x^2+1\right)^2-\left(2x\right)^2\)

\(=\left(2x^2+1-2x\right)\left(2x^2+1+2x\right)\)