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Algebra Difficulty 2.3 Junior Find the answer

Factorize:
(1) 2x4−22x^4-2;
(2) x4−18x2+81x^4-18x^2+81;
(3) (y2−1)2+11(1−y2)+24(y^2-1)^2+11(1-y^2)+24.

A number or a short expression. Spacing and $ signs are ignored.

Solution

Solution:
(1) The original expression can be rewritten as 2(x4−1)=2(x2+1)(x+1)(x−1)2(x^4-1)=2(x^2+1)(x+1)(x-1);
(2) The original expression can be rewritten as (x2−9)2=(x+3)2(x−3)2(x^2-9)^2=(x+3)^2(x-3)^2;
(3) The original expression can be rewritten as (y2−1−3)(y2−1−8)=(y2−4)(y2−9)=(y+2)(y−2)(y+3)(y−3)(y^2-1-3)(y^2-1-8)=(y^2-4)(y^2-9)=(y+2)(y-2)(y+3)(y-3).

Therefore, the factorized forms are:
(1) 2(x2+1)(x+1)(x−1)\boxed{2(x^2+1)(x+1)(x-1)};
(2) (x+3)2(x−3)2\boxed{(x+3)^2(x-3)^2};
(3) (y+2)(y−2)(y+3)(y−3)\boxed{(y+2)(y-2)(y+3)(y-3)}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.