Question

Докажите тождество (в)

Answer 1

a)=> (a²-4b²)(a²+4b²)=$a^{4}-16b^{4}$

b)=>(x²-1)(x²+1)=>$(x^{4}-1)(x^{4}+1)$=>$x^{8}-1$

c)=>$(a^{3}-8)(a^{3}+8)=>a^{6}-64$

d)=>$c^{4}+c^{3}-2c^{2}-c^{3}-c^{2}+2c-2c^{2}-2c+4=>c^{4} -5c^{2}+4$

Answer 2

в)

$(a-2)(a+2)(a^2-2a+4)(a^2+2a+4)=\\\\=\underbrace {(a-2)(a^2+2a+4)}_{a^3-2^3}\underbrace {(a+2)(a^2-2a+4)}_{a^3+2^3}=\\\\=(a^3-8)(a^3+8)=(a^3)^2-8^2=a^6-64$