Question

a) x^2 - 2xy + y^2 - z^2
b) x^8 + x^4 + 1
c) x^4 + 4^2
d) 4x^4 + 81
e) x(x + 4)(x + 6)(x + 10) + 128

Answer 1

a: \(=\left(x-y\right)^2-z^2=\left(x-y-z\right)\left(x-y+z\right)\)

b: \(=x^8+2x^4+1-x^4\)

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

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

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

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

d: \(=4x^4+81+36x^2-36x^2\)

\(=\left(2x^2+9\right)^2-36x^2\)

\(=\left(2x^2-6x+9\right)\left(2x^2+6x+9\right)\)

e: \(=\left(x^2+10x\right)\left(x^2+10x+24\right)+128\)

\(=\left(x^2+10x\right)^2+24\left(x^2+10x\right)+128\)

\(=\left(x^2+10x+8\right)\left(x^2+10x+16\right)\)

\(=\left(x^2+10x+8\right)\left(x+2\right)\left(x+8\right)\)