Răspuns:
Explicație pas cu pas:
a) a⁴+a²+1 = a⁴+2a²+1-a² = (a²+1)²-a² = (a²-a+1)(a²+a+1)
b) x⁴+x²y²+y⁴ = x⁴+2x²y²+y⁴-x²y² = (x²+y²)²-(xy)² =
= (x²-xy+y²)(x²+xy+y²)
c) a⁴+2a²+9 = a⁴+6a²-4a²+9 = (a²+3)²-4a² =
= (a²+3)-(2a)² = (a²-2a+3)(a²+2a+3)
d) x⁴+1 = x⁴+2x²-2x²+1 = (x²+1)²-2x² = (x²+1)²-(x√2)²=
= (x²-x√2+1)(x²+x√2+1)
e) x⁴+y⁴ = x⁴+2x²y²+y⁴-2x²y² = (x²+y²)²-(xy√2)² =
= (x²-xy√2+y²)(x²+xy√2+y²)
f) x⁴-x²+1 = x⁴+2x²+1-3x² = (x²+1)²-3x² =
= (x²-x√3+1)(x²+x√3+1)
Am folosit formulele :
a²+2ab+b² = (a+b)²
a²-b² = (a-b)(a+b)
