簡易多項式問題~~

1.展開下列各數式

a) (x-y)(x+2y)
= x^2+2xy-xy-2y^2
= x^2+xy-2y^2

b) (2m-5)(m-4)
= 2m^2-8m-5m+20
= 2m^2-13m+20

2.化簡下列各數式
a) (3x+2)+(2x-3)+(-x+5)
= 3x+2+2x-3-x+5
= 4x+4

b) (7x-2y)-(4x+5y)
=7X - 2Y - 4X -5Y
=3X - 7Y

c) (-a^2 + 3a-4)-(a^2 - a +1)
= -a^2+3a-4-a^2+a-1
= -2a^2+4a-5

d) (2x-3x^2 + 4 + 7x^3) - (4x^2 + 3x + 2x^2 - 6)
= 2x-3x^2 + 4 + 7x^3 - 4X^2 - 3X - 2x^2 + 6
= 7x^3 - 9X^2 -X + 10

3.展開(3x-2y)(2x+3y)
= 6x^2 + 9xy - 4xy - 6y^2
= 6x^2 + 5xy - 6y^2

4. 化簡 -3x^2 (2x-5)+4x(3x^2 + 1)
= -6X*3 + 15X*2 + 12X*3 + 4X
= 6X*3 + 15X*2 + 4X

5.展開(3x-1)(2x^2 + x -1)
= 6x^3 + 3x^2 - 3x - 2x^2 - x +1
= 6 x^3 + x^2 - 4x + 1

6. 展開
a.. (x+y)(x^2+ xy + y2)
= x^3 + x^2y + xy^2 + x^2y + xy^2 +y^3
= x^3 + y^3 + 2x^2y + 2xy^2

b.. (x-y)(x^2 + xy + y2)
= x^3 + x^2y +xy^2 - x^2y - xy^2 - y^3
= x^3 - y^3

c.. (x-y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)
= x^5 + x^4y + x^3y^2 + x^2y^3 +xy^4 - x^4y - x^3y^2 -x^2y^3 -xy^4 - y^5
= x^5 - y^5

7. 展開下列各式

a...(a+b+1)(a+b-1) 提示: 設 x = a+b
(x+1) (x-1) = x^2 - x + x -1
= x^2-1

b...(a+b+c+d)(a+b-c-d) 提示: 設x = a+b 及 y = c+d
(a+b+c+d) (a+b- (c+d) )
=(x+y) (x-y)
= x^2 - y^2

c...(x^2 + x + 1)(x^2 - x +1) 提示: 設y = x^2 +1
(x^2 + 1 + x)(x^2 + 1 - x)
= ( y + x ) ( y - x )
= y^2 - xy + xy - x^2
= y^2 - x^2


8. 改正以下列計算中的錯誤..

a...(x+y)^2 = x^2 + y^2
(x+y)^2 = x^2 + 2xy + y^2

b) 2乘[(2a)乘(3b)]= 2乘(2a)乘2乘(3b)
2[(2a)(3b)] = 2 [ 6ab ]
= 12 ab


9. 己知一個多項式乘以x-2..所得的乘積含有 -3x^2這個項..球該多項式..{注意:答案多於一個}

唔明白題目