Question

Помогите. Докажите тождество:

Answer 1

1)(x-y)²-(x-y)(y+x)=(x-y)(x-y-y-x)=(x-y)(-2y)=2y(y-x)
2)(1-c)(1-c²)+c(c+1)=(1-c)(1+c)(1-c)+c(c+1)=(c+1)((1-c)(1-c)+c)=
=(c+1)(1-2c+c²+c)=(c+1)(1-c+c²)=c³+1
3)(xy-1)²+(x+y)²=x²y²-2xy+1+x²+2xy+y²=x²y²+1+x²+y²=x²y²+x²+y²+1=
=x²(y²+1)+(y²+1)=(y²+1)(x²+1)