Question

用简便方法计算下面的算式:(14+28+39)*(28+39+15)—(14+28+39+15)*(28+39)一定要说出简便计算的思路！

Answer 1

将28+39直接算出得67，或者看成整体X，然后分解得：
(14+x)*(X+15)-(14X+15X+XX)
前面的括号依次乘开：
=(14X+15X+XX+14*15)-(14X+15X+XX)
减去相同项
=14*15

Answer 2

设15+28+39=X
则14+28+39=X-1 14+28+39+15=X+14 28+39=X-15
(14+28+39)*(28+39+15)—(14+28+39+15)*(28+39)
=(X-1)*X-(X+14)(X-15)
=X^2-X-X^2+X+14*15
=210

追问

我是四年级的小学生，能不用X解答吗？

追答

(14+28+39)*(28+39+15)—(14+28+39+15)*(28+39)
=[(28+39)+14]*[(28+39)+15]-[28+39)+29](28+39)
=(28+39)^2+29(28+39)+14*15-(28+39)^2-29*(28+39)
=14*15
=210

追问

^是什么意思啊？

追答

乘方，^2就是平方

Answer 3

(14+28+39)*(28+39+15)—(14+28+39+15)*(28+39)
设A=14+28+39 B=28+39

原式=A*(B+1)-(A+1)*B
=AB+A-AB-B
=A-B
=14+28+39-(28+39)
=14

Answer 4

=(14+28+39)[(28+39+15)—(28+39)])—15(28+39)
=14(14+28+39)—15(28+39)
=14*14)+(28+39)(14-15)
=196-67
=129