Question

разложите на множители :
1) c^2-x^2+2xy-y^2
2) 16-(x-5)^2
3) (x-5)^2-16

Answer 1

Ответ:

$1)(c-x+y)(c+x-y);\ 2)(9-x)(x-1);\ 3)(x-9)(x-1).$

Пошаговое объяснение:

$1)c^{2}-x^{2}+2xy-y^{2}=c^{2}-(x^{2}-2xy+y^{2})=c^{2}-(x-y)^{2}\\c^{2}-(x-y)^{2}=(c-(x-y))(c+(x-y))=(c-x+y)(c+x-y)\\\\2)16-(x-5)^{2}=4^{2}-(x-5)^{2}=(4-(x-5))(4+(x-5))=(9-x)(x-1)\\\\3)(x-5)^{2}-16=(x-5)^{2}-4^{2}=(x-5-4)(x-5+4)=(x-9)(x-1)$