平方差公式1[下学期]

课件13张PPT。平方差公式乘法公式：(x+a)(x+b)=x2+(a+b)x+ab(a+b)(a-b)=a2-b2——平方差公式1.当a=-b时1.下列多项式相乘，哪些可用平方差
公式？怎样用公式计算？
1) (a+b)(-b+a) 2) (ab+1)(-ab+1)
3) (a+b)(b-c) 4) (-2xy+z)(-2xy-z)
5) (a+b)(-a-b) 6) (a2-3bc)(3bc+a2)2.(a+b+c)(a+b-c),是否可用平方差公式计
算？怎样应用公式计算？2.(a+b+c)(a+b-c),是否可用平方差公式计
算？怎样应用公式计算？解： (a+b+c) (a+b-c)
= [(a+b)+c] [(a+b)-c]
= (a+b)2 - c2
= (a+b) (a+b) – c2
= (a2+ab+ab+b2) – c2
= (a2+2ab+b2) – c2
= a2+2ab+b2 – c23.将下列各式变形为可利用平方差公式
计算的形式：
1) (a+2b+3)(a+2b-3)
2) (a+2b-3)(a-2b+3)
3) (a-2b+3)(a-2b-3)
4) (a-2b-3)(a+2b-3)
5) (3a-5b-2c)(-3a-5b+2c)
6) (x+y+m+n)(x+y-m-n)[(a+2b)+3][(a+2b)-3][a+(2b-3)] [a-(2b-3)][(a-2b)+3] [(a-2b)-3][(a-3)-2b] [(a-3)+2b][(-5b)+(3a-2c)] [(-5b)-(3a-2c)][(x+y)+(m+n)][(x+y)-(m+n)]4.下列各式哪些能用平方差公式计算？
怎样用？
1) (a-b+c)(a-b-c)
2) (a+2b-3)(a-2b+3)
3) (2x+y-z+5)(2x-y+z+5)
4) (a-b+c-d)(-a-b-c-d)4.下列各式哪些能用平方差公式计算？
怎样用？
1) (a-b+c)(a-b-c) 解： 1) (a-b+c)(a-b-c)
= [ (a-b)+c] [ (a-b)-c ]
= (a-b)2 – c2
= (a2-2ab+b2) –c2
= a2-2ab+b2 –c24.下列各式哪些能用平方差公式计算？
怎样用？
2) (a+2b-3)(a-2b+3)解：2) (a+2b-3)(a-2b+3)
= [ a+(2b-3) ] [ a-(2b-3)]
= a2- (2b-3)2
= a2- (2b-3) (2b-3)
= a2- (4b2-12b+9)
= a2- 4b2+12b-94.下列各式哪些能用平方差公式计算？
怎样用？
3) (2x+y-z+5)(2x-y+z+5)
4) (a-b+c-d)(-a-b-c-d)解: 3) (2x+y-z+5)(2x-y+z+5)
= [ (2x+5)+(y-z) ] [(2x+5)-(y-z) ]
= (2x+5)2- (y-z)2 =……解: 4) (a-b+c-d)(-a-b-c-d)
= [ (-b-d)+(a+c) ] [(-b-d)-(a+c) ]
= (-b-d)2- (a+c)2 =……5.计算：
1) (y+2)(y-2) - (3-y)(3+y)
2) –3x(x+1)(x-1) - x(3x+2)(2-3x)
3) –4(2y- )( +2y) + 3(2y-3)(2y+1)
4) (x+ )(x2+ )(x- )解：1) (y+2)(y-2) - (3-y)(3+y)
= (y2-4) –(9-y2)
= y2-4 –9+y2
= 2y2-135.计算：
1) (y+2)(y-2) - (3-y)(3+y)
2) –3x(x+1)(x-1) - x(3x+2)(2-3x)
3) –4(2y- )( +2y) + 3(2y-3)(2y+1)
4) (x+ )(x2+ )(x- )解：2) –3x(x+1)(x-1) - x(3x+2)(2-3x)
= –3x(x2-1) - x(4-9x2)
= –3x3+3x – 4x+9x3
= 6x3-x5.计算：
1) (y+2)(y-2) - (3-y)(3+y)
2) –3x(x+1)(x-1) - x(3x+2)(2-3x)
3) –4(2y- )( +2y) + 3(2y-3)(2y+1)
4) (x+ )(x2+ )(x- )= -16y2+1+12y2-12y-9= -4y2-12y-8解:3) –4(2y- )( +2y) + 3(2y-3)(2y+1)= -4(4y2- )+3(4y2+2y-6y-3)5.计算：
1) (y+2)(y-2) - (3-y)(3+y)
2) –3x(x+1)(x-1) - x(3x+2)(2-3x)
3) –4(2y- )( +2y) + 3(2y-3)(2y+1)
4) (x+ )(x2+ )(x- )解：4) (x+ )(x2+ )(x- )= [(x+ )(x- )](x2+ )= (x2- )(x2+ )= x4-