Question

Докажите тождество:
1) x^4-(x^2-1)(x^2+1)=1;
2) (x-5)(x+8)-(x+4)(x-1)=-36.

Answer 1

1) x^4-(x^2-1)(x^2+1)=x^4-(x^4-1^2)=x^4-x^4+1=1
2) (x-5)(x+8)-(x+4)(x-1)=(x^2+8x-5x-40)-(x^2-x+4x-4)=x^2+8x-5x-40-x^2+x-4x+4=8x-5x-40+x-4x+4=3x-36+x-4x=4x-36-4x=-36