(3x^3y^2+6x^2y^3)/(x+2y)(-9m^2+4n^2)/(3m+2n)(4a^2-20ab+25b^2)/(5b-2a)(1-16a^4)/(4a^2+1)/(2a+1)

3x^2y^2(x+2y)/(x+2y)=3x^2y^2
=(2n)^2-(3m)^2/(3m+2n)
=(2n+3m)(2n-3m)/(3m+2n)
=(2n-3m)
=(5b-2a)^2/(5b-2a)
=5b-2a
=(1-4a^2)(1+4a^2)/[(4a^2+1)(2a+1)]
=(1-2a)(1+2a)/(2a+1)
=1-2a

(1)
(3x^3y^2+6x^2y^3)/(x+2y) (分子提出公因子 3x^2y^2)
=3x^2y^2(x+2y)/(x+2y)
=3x^2y^2
(2)
(-9m^2+4n^2)/(3m+2n) (分子用平方差公式)
=(2n+3m)(2n-3m)/(3m+2n)
=2n-3m
(3)
(4a^2-20ab+25b^2)/(5b-2a) (分子用完全平方公式)
=(2a-5b)^2/(5b-2a)
=(5b-2a)^2/(5b-2a)
=5b-2a
(4)
(1-16a^4)/(4a^2+1)/(2a+1) (对 1-16a^4 用平方差公式)
=(1+4a^2)(1-4a^2)/[(4a^2+1)(2a+1)]
=(1-4a^2)/(2a+1) (再对 1-4a^2 用平方差公式)
=(1+2a)(1-2a)/(2a+1)
=1-2a