Докажите тождество: 1) (a+2b) (a - 2b) (a^2+4b^2) = a^4 - 16b^42) (x-1) (x+1) (x^2+1) (x^4+1) = x^8 - 13) (a-2) (a+2) (a^2 - 2a + 4) (a^2 + 2a + 4) = a^6 - 644) (с^2-c-2) (c^2+c-2) = c^4 - 5c^2 + 4

Докажем тождества:

1) (a + 2 * b) * (a - 2 * b) * (a^2 + 4 * b^2) = a^4 - 16 * b^4;

(a^2 - 4 * b^2) * (a^2 + 4 * b^2) = a^4 - 16 * b^4;

a^4 - 16 * b^4;

Верно.

2) (x - 1) * (x + 1) * (x^2 + 1) * (x^4 + 1) = x^8 - 1;

(x^2 - 1) * (x^2 + 1) * (x^4 + 1) = x^8 - 1;

(x^4 - 1) * (x^4 + 1) = x^8 - 1;

x^8 - 1 = x^8 - 1;

Верно.

3) (a - 2) * (a + 2) * (a^2 - 2 * a + 4) * (a^2 + 2 * a + 4) = a^6 - 64;

(a^2 - 4) * (a^2 - 2 * a + 4) * (a^2 + 2 * a + 4) = a^6 - 64;

(a^2 - 4) * ((a^2 + 4) ^2 - 4 * a^2) = a^6 - 64;

(a^2 - 4) * (a^4 + 8 * a^2 + 16 - 4 * a^2) = a^6 - 64;

(a^2 - 4) * (a^4 + 4 * a^2 + 16) = a^6 - 64;

a^6 - 64 = a^6 - 64;

Верно.

4) (с^2 - c - 2) * (c^2 + c - 2) = c^4 - 5 * c^2 + 4;

(c^2 - 2) ^2 - c^2 = c^4 - 5 * c^2 + 4;

c^4 - 4 * c^2 + 4 = c^4 - 5 * c^2 + 4;

c^4 - 5 * c^2 + 4 = c^4 - 5 * c^2 + 4;

Верно.