Question

Разложите многочлен на множители:
1) х^4-3х^2+2
2)у^2-10у+25-4х^2
3)х^16-у^16

Answer 1

$x^4-3x^2+2=(x^2-1)(x^2-2)=(x-1)(x+1)(x^2-2)\\y^2-10y+25-4x^2=(y-5)^2-4x^2=(y-5-2x)(y-5+2x)\\x^{16}-y^{16}=(x^8-y^8)(x^8+y^8)=(x^4-y^4)(x^4+y^4)(x^8+y^8)=\\=(x^2-y^2)(x^2+y^2)(x^4+y^4)(x^8+y^8)=\\=(x-y)(x+y)(x^2+y^2)(x^4+y^4)(x^8+y^8)$