(2.15﹢5.17+3.62)×(5.17+2.15+8.5)-(3.62+2.15+8.5+5.17)×(2.15+5.17)用简便方法计算

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/12 05:12:51

(2.15﹢5.17+3.62)×(5.17+2.15+8.5)-(3.62+2.15+8.5+5.17)×(2.15+5.17)用简便方法计算
(2.15﹢5.17+3.62)×(5.17+2.15+8.5)-(3.62+2.15+8.5+5.17)×(2.15+5.17)用简便方法计算

(2.15﹢5.17+3.62)×(5.17+2.15+8.5)-(3.62+2.15+8.5+5.17)×(2.15+5.17)用简便方法计算
原式=[(2.15+5.17)+3.62]×[(2.15+5.17)+8.5]-[3.62+8.5+(2.15+5.17)]×(2.15+5.17)
=(2.15+5.17)²+3.62×(2.15+5.17)+8.5×(2.15+5.17)+3.62×8.5-[3.62×(2.15+5.17)+8.5×(2.15+5.17)+(2.15+5.17)²]
=(2.15+5.17)²+3.62×(2.15+5.17)+8.5×(2.15+5.17)+3.62×8.5-3.62×(2.15+5.17)-8.5×(2.15+5.17)-(2.15+5.17)²
=3.62×8.5
=3.62×(9-0.5)
=3.62×9-3.62×0.5
=32.58-1.81
=30.77
或者:
令a=2.15+3.17
原式=(a+3.62)×(a+8.5)-(3.62+8.5+a)×a
=a²+3.62a+8.5a+3.62×8.5-(3.62a+8.5a+a²)
=a²+3.62a+8.5a+3.62×8.5-3.62a-8.5a-a²
=3.62×8.5
=3.62×(9-0.5)
=3.62×9-3.62×0.5
=32.58-1.81
=30.77