Question

应用乘法公式计算（中学）

1、（2a3－3b2）(3b2—2a3)
2、（c-2b+3a）(2b+c-3a)
3、(a2-4b2)(a2+2ab+4b2)(a2-2ab+4b2)

Answer 1

1原式=-(2a3-3b2)(2a3-3b2)=-(2a3-3b2)2=-4a6+12a3b2-9b4
2原式=(c+(3a-2b))(c-(3a-2b))=c2-(3a-2b)2=c2-9a2+4b2
3、原式=(a2-4b2)(a2+4b2+2ab)(a2+4b2-2ab)
=(a2-4b2)[(a2+4b2)2-4a2b2]
=(a2-4b2)(a2+4b2)2-(a2-4b2)4a2b2
=(a4-16b4)(a2+4b2)-4a4b2+16a2b4
=a6+4a4b2-16a2b4-64b6-4a4b2+16a2b4
=a6-64b6

Answer 2

1:(2a3-3b2)(3b2-2a3)
=-(2a3-3b2)(2a3-2b2)
=-(2a3-2b2)2
=-[(2a3)2+(3b2)2-2*2a3*3b2]
=-(4a6+9b4-12a3b2)
=-4a6-9b2+12a3b2
2:、（c-2b+3a）(2b+c-3a)
=[c-(2b)2+(3a)2][c+(2b-3a)]
=c2-[(2b2)+(3a)2-2*2b*3a]
=c2-(4b2+9a2-12ab)
=c2-4b2-9a2+12ab
3:a6+32a2b4-8a4b2-64b6