初中数学湘教版（2024）七年级下册（2024）1.1 整式的乘法教学课件ppt

这是一份初中数学湘教版（2024）七年级下册（2024）1.1 整式的乘法教学课件ppt，共19页。PPT课件主要包含了-x5，1a24，a2xnyn，9x2+7x-1，课堂小结等内容，欢迎下载使用。
(1) a2·a3=______
(2) x·x3 ·x4 =______
(3) (-x)2·(-x)3 =______
(4) (-a)3·(-a)2 ·(-a) =______
(2) (-xm)5(m是正整数)
(3) -(3xy3)2
(4) (p2q)n(n是正整数)
(1) (a2)4=a8
(2) (-xm)5= -x5m
(3) -(3xy3)2=-9x2y6
(4) (p2q)n= p2nqn
(1) (2×105)×(3×106)
(2) (1.2×104)×(-2.5×107)
= (2×3)×(105×106)
= 1.2×(-2.5)×(104×107)
4.从太阳系外距地球最近的一颗恒星(比邻星)发出的光，大约需要4.2年时间才能到达地球。光的速度约为3×108m/s,1年以3.15×107s计算，求这颗恒星与地球的大概距离。
3.15×107×4.2×3×108=3.969×1016(m)
答：这颗恒星与地球的大概距离3.969×1016m。
(1) 2x3·3xy
(2) 4x2y·(-5xy2)
(3) axn-1y·axyn-1(其中a是非零常数，n>1，且n是正整数)
4x2y·(-5xy2)
axn-1y·axyn-1
(1) (2x2y-xy)·3xy
(2x2y-xy)·3xy
= 2x2y ·3xy -xy ·3xy
= 6x3y2 -3x2y2
(3) 3x2·(-2xy)2-x3·(xy2-2)
(4) 4x·(x2y-xy2)-3y·(5x3+x2y)
3x2·(-2xy)2-x3·(xy2-2)
= 3x2·4x2y2-x3·xy2+2x3
= 12x4y2-x4y2+2x3
= 11x4y2+2x3
4x·(x2y-xy2)-3y·(5x3+x2y)
=4x·x2y- 4x·xy2-3y·5x3-3y·x2y
=4x3y- 4x2y2-15x3y-3x2y2
=-11x3y-7x2y2
(1) (3x+2y)(7x-6y)
(2) (2x-5y)(2xy-3y2)
(3x+2y)(7x-6y)
=3x(7x-6y) +2y (7x-6y)
=3x·7x- 3x·6y +2y·7x- 2y· 6y
=21x2- 18xy +14xy- 12y2
=21x2- 4xy -12y2
(2x-5y)(2xy-3y2)
= 2x(2xy-3y2) -5y(2xy-3y2)
= 2x·2xy- 2x·3y2-5y·2xy+5y·3y2
= 4x2y-6xy2-10xy2+15y3
= 4x2y-16xy2+15y3
(3) (4x+3y)(x-2y)-(3x-2y)·x
(4x+3y)(x-2y)-(3x-2y)·x
= 4x(x-2y)+3y(x-2y) -(3x-2y)·x
= 4x·x-4x·2y+3y·x-3y·2y-3x·x+2y·x
= 4x2-8xy+3xy-6y2-3x2+2xy
= x2-3xy-6y2
(4) 2x·(x2-4x)-(x2+1)(2x-3)
2x·(x2-4x)-(x2+1)(2x-3)
= 2x·(x2-4x)-x2(2x-3)-(2x-3)
= 2x·x2- 2x·4x-x2·2x+3x2-2x+3
= 2x3-8x2-2x3+3x2-2x+3
= -5x2-2x+3
8. (1)计算 (2x-y)(3x+2y)-(4x-3y)(2x-5y)
(2x-y)(3x+2y)-(4x-3y)(2x-5y)
= 2x(3x+2y)-y(3x+2y)-4x(2x-5y)+3y(2x-5y)
= 2x·3x+ 2x·2y-y·3x-y·2y-4x·2x+4x·5y+3y·2x- 3y· 5y
= 6x2+4xy-3xy-2y2-8x2+20xy+6xy-15y2
= -2x2+27xy-17y2
-2x2+27xy-17y2
9.一个长方体的长是2.4×104cm，宽是1.5×103cm，高是0.6×103cm，求这个长方体的体积及表面积。
V= 2.4×104×1.5×103×0.6×103=2.16×1010(cm3)
S = 2×2.4×104×1.5×103+2×2.4×104×0.6×103+2×1.5×103×0.6×103=1.026×108(cm2)
答：这个长方体的体积为2.16×1010cm3,表面积为1.026×108cm2。
(1) ( )·(-3xy)=-15x2y3
(2) 2ab·( )=-8a2bc
(3) (-x2)·( )=7x2y
(4) (a2)2·( )= -2a5b
11.下列计算对不对？如果不对应该怎样改正？
(1) [(a+b)2]3= (a+b)5
(2) -[-(x+y)3]2= (x+y)6
(1) [(a+b)2]3= (a+b)6
(2) -[-(x+y)3]2= -(x+y)6
(1) (x2+2x+2)(x+2)+(-x2+1)(x-5)
(x2+2x+2)(x+2)+(-x2+1)(x-5)
=x2(x+2)+2x(x+2)+2(x+2)-x2 (x-5) +(x-5)
=x3+2x2+2x2+4x+2x+4-x3+5x2+x-5
(2) (x+2y)(2x-2y)+(2x-2y)(3x+2y)-8(x2-y2)
(x+2y)(2x-2y)+(2x-2y)(3x+2y)-8(x2-y2)
= [(x+2y)+(3x+2y)](2x-2y)-8(x2-y2)
= (4x+4y)(2x-2y)-8(x2-y2)
= 4x(2x-2y)+4y(2x-2y)-8x2+8y2
= 8x2-8xy+8xy-8y2-8x2+8y2