Докажите тождество: a)(a^2+4)^2-16a^2=(a+2)^2(a-2)^2 б)(x^2+3)^2=(x^2-3)(x^2+3)+6(x^2+3)

Question

Докажите тождество: a)(a^2+4)^2-16a^2=(a+2)^2(a-2)^2 б)(x^2+3)^2=(x^2-3)(x^2+3)+6(x^2+3)

Answer 1

a^4+16+8a^2-16a^2=(a^2-4)^2=(a-2)^2(a+2)^2

(x^4+9+6x^2)=(x^4-9)+(18+6x^2)=(x^2-3)(x^2+3)+6(3+x^2)