Question

Разложите многочлен на множители а)x^2-y^2-10x-12y-11

Answer 1

x²-y²-10x-12y-11=(x²-10x+25)-25-y²-12y+
36-36-11=

(x-5)²-(y+6)²=(x-5+y+6)(x-5-y-6)=

(x+y+1)(x-y-11)

Answer 2

x^2-y^2-10x-12y-11=x^2-10x+25-25-(y^2+12y+36-36)-11=(x-5)^2-25-(y+6)^2+36-11=(x-5)^2-(y+6)^2=(x-5+y+6)(x-5-y-6)=(x+y+1)(x-y-11),  использовали формулу

a^2-b^2=(a-b)(a+b)