因式分解：① (x+y)^2-(3x-2y)^2 ②9(2a+3b)^2-25(3a-b)^2 ③a^3+4a^2b+4ab^2 （每道题要过程,谢谢）

a^3-4a^2b+4ab^2 =a(a^2-4ab+4b^2)=a(a-2b)^2 2:4y^2-(2z-x)^2=(2y+2z-x)(2y-2z+x) 3.:4x^2-y^2

① (x+y)^2-(3x-2y)^2
=x^2+2xy+y^2-(9x^2-12xy+4y^2)
=-8x^2+14xy-3y^2
=-(8x^2-14xy+3y^2)
=-(2x-3y)(4x-y)
②9(2a+3b)^2-25(3a-b)^2
=9(4a^2+12ab+9b^2)-25(9a^2-6ab+b^2)
=36a^2+108ab+81b^2-225a^2+150ab-25b^2
=-189a^2+258ab+56b^2
=-(189a^2-258ab-56b^2)
=-(9a-14b)(21a+4b)
③a^3+4a^2b+4ab^2
=a*(a^2+4ab+4b^2)
=a*(a+2b)^2
祝你开心！希望能帮到你，如果不懂，请追问，祝学习进步！O(∩_∩)O

①(x+y)²-(3x-2y)²=[(x+y)+(3x-2y)][(x+y)-(3x-2y)]=(4x-y)(-2x+3y)②9(2a+3b)²-25(3a-b)²=[3(2a+3b)+5(3a-b)][3(2a+3b)-5(3a-b)]=(21a+4b)(-9a+14b)③a³+4a²b+4ab²=a(a²+4...

1、
原式=[(x+y)-(3x-2y)]*[(x+y)+(3x-2y)]=(3y-2x)(4x-y)
2、
原式=[3(2a+3b)-5(3a-b)]*[3(2a+3b)+5(3a-b)]=(14b-9a)(21a+4b)
3、
原式=a(a²+4ab+4b²)=a(a+2b)²
祝你开心！希望能帮到你，如果不懂，请追问，祝学习进步！O(∩_∩)O