(5x^3-3y^3)^2-(3x^3-5y^3)^2

题目

(5x^3-3y^3)^2-(3x^3-5y^3)^2
3a(b^2+9)^2-108ab^2
676^3+676* 324* 352-324^3
-3x^3-81y^3
4x^2y^2-(x^2+y^2)^2
(4a^2-9b^2)+(4a+3b)
...

答案

1、
(5x^3-3y^3)^2-(3x^3-5y^3)^2
＝〔(5x^3-3y^3)+(3x^3-5y^3)〕〔(5x^3-3y^3)-(3x^3-5y^3)〕
= (8x^3-8y^3)(2x^3+2y^3)
=8(x^3-y^3)*2(x^3-y^3)
=16(x^6-y^6)
2、
3a（b^2 +9）^2-108ab^2
=3a[(b^2+9)^2-36b^2]
=3a(b^2+9+6b)(b^2+9-6b)
=3a(b+3)^2(b-3)^2
3、
676^3+676*324*352-324^3
=676^3+676*324*(676-324)-324^3
=676^3+676^2*324-676*324^2-324^3
=676^3-3*676^2*324+3*676*324^2-324^3+4*676^2*324-4*676*324^2
=(676-324)^3+4*676*324*(676-324)
=352^3+4*676*324*352
=352(352^2+4*676*324)
=352000000
4、
-3x^3-81y^3
=-3x^3-3*3^3y^3
=-3(x^3-(3y)^3)
=-3(x-3y)(x^2+xy+(3y)^2)
5、
4x^2y^2-(x^2+y^2)^2
=4x^2y^2-x^4-2x^2y^2y^2-y^4
=-x^4+2x^2y^2y^2-y^4
=-(x^2-y^2)^2
6、
(4a^2-9b^2)+(4a+3b)
这道题你没有抄错吧!