Восьмой вариант со второго задания

Question

Алгебра: Восьмой вариант со второго задания

Катюша1233210 · Accepted Answer

(a-x)(x³-y³)-(x-y)(a³-x³)=
=(a-x)(x-y)(x²+xy+y²)-(x-y)(a-x)(a²+ax+x²)=
=(a-x)(x-y)(x²+xy+y²-a²-ax-x²)=
=(a-x)(x-y)(y²-a²+xy-ax)

2x³-2xy²-6x²+6y²=
=(2x³-2xy²)-(6x²-6y²)=
=2x(x²-y²)-6(x²-y²)=
=(x²-y²)(2x-6)=
=2(x-3)(x-y)(x+y)

5a²-5b²-10a³b+10ab³=
=(5a²-5b²)-(10a³b-10ab³)=
=5(a²-b²)-10ab(a²-b²)=
=(a²-b²)(5-10ab)=
=5(1-5ab)(a-b)(a+b)

36x³-144x-36x²+144=
=(36x³-36x²)-(144x-144)=
=36x²(x-1)-144(x-1)=
=(x-1)(36x²-144)=
=(x-1)(6x-12)(6x+12)=
=(x-1)*6(x-2)*6(x+2)=
=36(x-1)(x-2)(x+2)

y³+ay²-b²y-b²a=
=(y³+ay²)-(b²y+b²a)=
=y²(y+a)-b²(y+a)=
=(y+a)(y²-b²)=
=(y+a)(y-b)(y+b)

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