11. 分解因式:
(1) $x^4 -81$;
(2) $4x^2 -64$;
(3) $(x+y)^2 - (a+b)^2$;
(4) $(a^2 +9)^2 -36a^2$;
(5) $(x^2 +4)^2 -16x^2$;
(6) $x^2 + y^2 +2xy -1$;
(7) $x^2(y^2 -1) +2x(y^2 -1)+(y^2 -1)$;
(8) $(m+n)^2 -4m(m+n)+4m^2$;
(9) $(x^2 -1)^2 +6(x^2 -1)+9$;
(10) $2x^3y -8x^2y^2 +8xy^3$。
(1) $x^4 -81$;
(2) $4x^2 -64$;
(3) $(x+y)^2 - (a+b)^2$;
(4) $(a^2 +9)^2 -36a^2$;
(5) $(x^2 +4)^2 -16x^2$;
(6) $x^2 + y^2 +2xy -1$;
(7) $x^2(y^2 -1) +2x(y^2 -1)+(y^2 -1)$;
(8) $(m+n)^2 -4m(m+n)+4m^2$;
(9) $(x^2 -1)^2 +6(x^2 -1)+9$;
(10) $2x^3y -8x^2y^2 +8xy^3$。
答案
(1) $(x^2+9)(x+3)(x-3)$
(2) $4(x+4)(x-4)$
(3) $(x+y+a+b)(x+y-a-b)$
(4) $(a+3)^2(a-3)^2$
(5) $(x+2)^2(x-2)^2$
(6) $(x+y+1)(x+y-1)$
(7) $(y+1)(y-1)(x+1)^2$
(8) $(n-m)^2$
(9) $(x^2+2)^2$
(10) $2xy(x-2y)^2$
(2) $4(x+4)(x-4)$
(3) $(x+y+a+b)(x+y-a-b)$
(4) $(a+3)^2(a-3)^2$
(5) $(x+2)^2(x-2)^2$
(6) $(x+y+1)(x+y-1)$
(7) $(y+1)(y-1)(x+1)^2$
(8) $(n-m)^2$
(9) $(x^2+2)^2$
(10) $2xy(x-2y)^2$
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