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20.(本小题6分)分解因式：
(1)$9x^2 -16y^2 =$
(2)$x^2 +2x -8 =$
(3)(要求写过程)$-4ax^2 +24axy -36ay^2$.
(1)$9x^2 -16y^2 =$
$(3x+4y)(3x-4y)$
.(2)$x^2 +2x -8 =$
$(x+4)(x-2)$
.(3)(要求写过程)$-4ax^2 +24axy -36ay^2$.
答案
20.【解】(1)$(3x+4y)(3x-4y)$
(2)$(x+4)(x-2)$
(3)原式=$-4a(x^2-6xy+9y^2)=-4a(x-3y)^2$.
(2)$(x+4)(x-2)$
(3)原式=$-4a(x^2-6xy+9y^2)=-4a(x-3y)^2$.
21.(本小题6分)计算：
答案
21.【解】(1)原式=$-\frac{a}{6b}·\frac{9b^2}{4a^2}=-\frac{3b}{8a}$.
(2)原式=$1-\frac{x+y}{x-2y}÷\frac{(x+y)(x-y)}{(x-2y)^2}=1-\frac{x+y}{x-2y}·\frac{(x-2y)^2}{(x+y)(x-y)}=1-\frac{x-2y}{x-y}=\frac{x-y-x+2y}{x-y}=\frac{y}{x-y}$.
(2)原式=$1-\frac{x+y}{x-2y}÷\frac{(x+y)(x-y)}{(x-2y)^2}=1-\frac{x+y}{x-2y}·\frac{(x-2y)^2}{(x+y)(x-y)}=1-\frac{x-2y}{x-y}=\frac{x-y-x+2y}{x-y}=\frac{y}{x-y}$.
