《代数式的值》ppt课件

.a2 b2 c2 2ab 2bc 2ac 的值吗？
它的值为
1
。
a2 b2 c2 2ab 2bc 2ac (a b c)2 (0.125 0.375 0.5)2 12 1
感悟：p89页议一议
填写下表，并观察下列两个代数式的值 的变化情况：
n 5n+6
n2
-3 -2 -1 0 1 2 3 4
-9 -4 1 6 11 16 21 26 9 4 1 0 1 4 9 16
⑴ 随着n 的值逐渐变大，两个代数式的值 如何变化？ ⑵ 估计一下，哪个代数式的值先超过100？
整体带入
（题源）若a+b=-1,求代数式 (1)a+b+2的值;
解:当a+b=-1时, a+b+2=-1+2=1 (2)3a+3b的值.
《数学》(七年级 上册)
用火柴棒按如下方式搭小鱼.
(1)搭n条小鱼用多少根火柴棒? (2)搭20条这样的小鱼用多少根火柴棒?
100条呢?
代数式的值: 根据问题的需要,用具体数值代替代
数式中的字母,按照代数式中的运算关系, 所得的结果是代数式的值.
例1.根据下列条件,求代数式 2a2 3ab b2
3x 6y2 4
=3x 2y2 +4（逆用乘法分配律）
32 4 10
(变题2)若2b-a=5，求代数式5(a-2b)2-3(a-2b)-60的值。
解：∵2b-a=5，∴a-2b=-5 ∴ 5(a-2b)2-3(a-2b)-60=5×(-5)2-3×(-5)-60 =125+15-60 =80
（1）设一个人质量为a千克，身高为h米，则他的身体质
方的商。一个健康人的身体质量指数在20~25之间。
况。这个指数是人体质量（千克）与人体身高（米）平
现代营养学家用身体质量指数来判断人体的健康状
a
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整体带入
(变题3)已知 y=ax³+bx+3，当 x=3时，y= -7， 试求：当 x= -3时，y 的值。
解：当x=3时， y = ax³+bx+3 = a·3³+b·3+3=-7 27a+3b+3=-7 27a+3b=-10 当 x= -3, 27a+3b=-10时 y = a·(-3)³+b·(-3)+3 = -27a+(-3b)+3 = -(27a+3b)+3 = -(-10)+3 = 13
练习:
某种药品的数量与总价关系如下表：
数量(克)
总价(元)
1
2.1 =2+0.1
2
4.1 =4+0.1
3
6.1 =6+0.1
4
8.1 =8+0.1
……
……
写出药品数量x（克）与总价y（元）之间的关系。
y=2x+0.1
h2 （2）某人的身高1.70米，体重62千克，则他的身体质量 （3指）数课为后请你估算一下你及你1；.67的202家人21.的45身32体87质2量指数。
a2 b2 c2 2ab 2bc 2ac
22 12 32 2 21 21 3 2 2 3
4 1 9 4 6 12 4
例2.当a 2，b 1，c 3时， 求下列各代数式的值：
1 b2 4ac; 2 a 2 b2 c2 2ab 2bc 2ac;
3 a b c2
的值.
(1) a= - 2 ,b= - 3; (2)a= 1 1 , b= 4
2
3
反思与总结：
（１）格式: “ 当 …… 时 ”
（２）代入时，数字要代入对应的字母的位置去；
（３）在求值时，原来省略的乘号要添上；
（ 4 ）若代入 的是负数或分数，必须加上括号。
（5）一般情况下,代数式中字母的值变化,代数式的 值也随之变化.
练一练：
若代数式2a2+3a+1的值为5，求代数式 4a2+6a+8的值.
解： 由2a2+3a+1+5，得2a2+3a=4. 当2a2+3a=4时，
4a2+6a+8=2(2a2+3a)+8 =2 Χ 4+8 =16
人体血液重量约占人体重的6%， 1、某人体重为a kg，那么血液重量约多少kg？
0.06a(kg) 2、亮亮的体重为35kg，它的血液量约多少kg呢？
(1)(a+2b)(a-2b) (2) a2 2b2
3.根据下列条件求代数式 x3 2x2 x
的值.
(1)x= 1 (2) x= - 2 2
例2.当a 2，b 1，c 3时， 求下列各代数式的值：
1b2 4ac; 2a 2 b 2 c 2 2ab 2bc 2ac; 3a b c2
35×0.06=2.1(kg)
3、请估计自己的血液重量。
一根弹簧，原长为12 cm，当弹簧受到拉力 F时（F在一定范围内），弹簧的长度用L表示。 测得的有关数据如下表所示：
拉力F(kg) 1 2 3 4 …
弹簧的长度L(cm) 12+0.5 12+1.0 12+1.5 12+2.0 …
（1）写出用拉力F表示弹簧长度L的关系式； （2）当弹簧受到6kg的拉力是，长度是多少？
解： 1当a 2，b 1，c 3时，
注意：一定要有这一步！！！
b2 4ac 12 4 2 3
1 24 25
Baidu Nhomakorabea
例2.当a 2，b 1，c 3时， 求下列各代数式的值：
1 b2 4ac; 2 a 2 b2 c 2 2ab 2bc 2ac; 3 a b c 2当a 2，b 1，c 3时， 2
辨析：
（1）判断题：
（ ）①当 x
1 2
时，3x 2
3 1 2 2
31 4
；
（）②当 x 2 时， 3x2 3 22 1
如何改正呢？
3x2
3
1
2
3
1
3
2 4 4
3x2 3 22 3 4 12
练一练:
1.当 x= - 2时,求代数式 x2 2x 1的值.
2.当a=5,b= - 2时,求下列代数式的值:
3当a 2，b 1，c 3时，
a b c2 2 1 32 4
观察（2）（3）两题的结果，你有什么想法？
a2 b2 c2 2ab 2bc 2ac =4
a b c2 a2 b2 c2 2ab 2bc 2ac
思考：
你能用简便方法算出当 a 0.125 , b 0.375 , c 0.5 时，
解:当a+b=-1时,
3a+3b=3(a+b)=3×(-1)=-3
(变题1)若 x 2 y 2 5 的值为7，求代数式
3x 6 y 2 4
的值。
整体带入
若 x 2y2 5 的值为7，求代数式 3x 6 y 2 4 的值。
解：由已知 x 2y2 5 7 ，则 x 2y2 2