Question

Докажите тождество:

1) (a+2b)(a - 2b)(a^2+4b^2) = a^4 - 16b^4
2) (x-1)(x+1)(x^2+1)(x^4+1) = x^8 - 1
3) (a-2)(a+2)(a^2 - 2a+ 4)(a^2 + 2a +4) = a^6 - 64
4) (с^2-c-2)(c^2+c-2) = c^4 - 5c^2 +4

Answer 1

1) (a^2-4b^2)(a^2+4b^2)=a^4-16b^4
2) (x^2-1)(x^2+1)(x^4+1)=(x^4-1)(x^4+1)=x^8-1
3) (a-2)(a+2)(a^2-2a+4)(a^2+2a+4)=(a^2-4)(a^4+4a^2+16)=a^6-64
4) (c^2-c-2)(c^2+c-2)=(c-2)*(c-1)*(c+1)*(c+2)=c^4-5c^2+4