Question

разложите на множители n^4-16, a^4-9a^2, x^4-x^8, a^9-1

Answer 1

1)  n^4-16=(n^2-4)(n^2+4)=(n-2)(n+2)(n^2+4)
2)  a^4-9a^2=a^2(a^2-9)=a^2(a-3)(a+3)
3)  x^4-x^8=-(x^8-x^4)=-x^4(x^4-1)=-x^4(x^2-1)(x^2+1)=-x^4(x^2+1)(x-1)(x+1)
4) a^9-1=(a^3-1)(a^6+a^3+1)=(a-1)(a^2+a+1)(a^6+a^3+1)

Answer 2

1) n^4 - 16 = (n^2 - 4)(n^2 + 4) = (n - 2)(n + 2)(n^2 + 4)

2) a^4 - 9a^2 = (a^2 - 3)(a^2 + 3) = (a - √3)(a + √3)(a^2 + 3)

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

4) a^9 - 1 = (a^3 - 1)(a^6 + a^3 + 1) = (a - 1)(a^2 + a + 1)(a^6 + a^3 + 1)