Надо разложите на множители. 1)x^8-y^8 2)x^2y+2xy^2+y^3 - вопрос №188222233224321532565027 от apetrochenkov 22.05.2022 17:47

Question

Алгебра: Надо разложите на множители. 1)x^8-y^8 2)x^2y+2xy^2+y^3 3)b^2-c^2-b+c 4)a^3+a^2-a-1 5)a^3+b^3-a^2b-ab^2 6)ax+ay-x^2-2xy-y^2 7)x^2(x-3)+10x(x-3)+25(x-3) 8)(a-x)(x^2--y)(a^2-x^2)

apetrochenkov · Answer

1)x^8-y^8 = (x⁴-y⁴)(x⁴+y⁴) = (x²-y²)(x²+y²)(x⁴+y⁴) = (x-y)(x+y)(x²+y²)(x⁴+y⁴).
2)x^2y+2xy^2+y^3 = y(x^2+2xy+y^2) = y(x+y)².
3)b^2-c^2-b+c = (b^2-c^2)-(b-c) - (b-c)(b+c)-(b-c) = (b-c)(b+c-1).
4)a^3+a^2-a-1 = a²(a+1) -(a+1) = (a+1)(a²-1) = (a+1)²(a-1).
5)a^3+b^3-a^2b-ab^2 = a²(a-b)-b²(a-b) = (a-b)²(a+b).
6)ax+ay-x^2-2xy-y^2 = a(x+y)-(x+y)² = (x+y)(a-x-y).
7)x^2(x-3)+10x(x-3)+25(x-3) = (x-3)(x+5)².
8)(a-x)(x^2-y^2)-(x-y)(a^2-x^2) = (a-x)(x-y)(x+y)-(x-y)(a-x)(a+x) =
= (a-x)(x-y)(x+y-a-x) = (a-x)(x-y)(y-a).