Question

Разложите на множители: д) а^6-2^6= e) x^6-1= разложите на множители: д) 1-c^4= e) x^2-16x^4=

Answer 1

Д) (a-2)^6
е) x^2(1+16x^2)

Answer 2

д) a^6 - 2^6 = (a^3)^2 - (2^3)^2 = (a^3 - 2^3)(a^3 + 2^3) = (a - 2)(a^2 + 2a + 4)(a + 2)(a^2 - 2a + 4)

e) x^6 - 1 = (x^3)^2 - 1^2 = (x^3 - 1)(x^3 + 1) = (x - 1)(x^2 + x + 1)(x + 1)(x^2 - x + 1)

д) 1 - c^4 = 1^2 - c^4 = (1 - c^2)(1 + c^2) = (1 - c)(1 + c)(1 - ic)(1 + ic)

e) x^2 - 16x^4 = x^2 - (4x^2)^2 = x^2 - (4x^2)^2 = x^2 - (4x^2)(4x^2) = x^2(1 - 16x^2) = x^2(1 - 4x)(1 + 4x)