很多 多項式的數不會做...Thanks~~

1)
28x2 - 28xy + 7y2
= 7 (4x2 - 4xy + y2)
= 7 (2x-y)2
[不是7(2x+y)2]

2)
(x-4)2 - 9(x+3)2
= (x-4)2 - (3x+9)2
= [(x-4)+(3x+9)] [(x-4)-(3x+9)]
= (4x+5) (-2x-13)
= - (4x+5) (2x+13)
[不是-(4x+5)(2x-13)]

3)
10(x+5)2 - 19(x+5) + 6
= [5(x+5)-2] [2(x+5)-3]
= (5x+25-2) (2x+10-3)
= (5x+23) (2x+7)

4)
a.
16a4 - b2
= (4a2 + b) (4a2 - b)

b.
16(x-1)4 - (x2 - 1)2
= [4(x-1)2 + (x2 - 1)] [4(x-1)2 - (x2 - 1)]
= [4(x-1)(x-1) + (x+1)(x-1)] [4(x-1)(x-1) - (x+1)(x-1)]
= (4x-4+x+1)(x-1) (4x-4-x-1)(x-1)
= (5x-3) (3x-5) (x-1)2

5)
a.
a(1-x)(1-2x) + b≡2x2 + cx - 9
a(2x2 -3x + 1) + b≡2x2 + cx - 9
2ax2 -3ax + (a+b)≡2x2 + cx - 9
比較其系數下：
a=1
a+b=-9
b=-9-a
b=-9-1
b=-10
c=-3a
c=-3

b.
40 - 4 (x - 1) (2x - 1)
= -4 [(1 - x) (1 - 2x) - 10]
= -4 (2x2 - 3x - 9)
= -4 (x-3) (2x-3)
[不是4(x-3)(2x-3)]

6)
a.
3x3 + 1/9
= 3 (x3 + 1/27)
= 3 (x + 1/3) (x2 - x/3 + 1/9)

b.
x5 y - 125x2 y4
= x2 y (x3 - 125y3)
= x2 y (x - 5y) (x2 + 5xy + 25y2)

7)
a10 + 4a9 - ab9 - 4b9
= a9 (a+4) - b9 (a+4)
= (a9 - b9) (a+4)
= (a3 - b3) (a6 + a3b3 +b6) (a+4)
= (a-b) (a2 + ab +b2) (a6 + a3b3 +b6) (a+4)

1) 28 x^2 - 28xy +7 y^2 = 7(4x^2 - 4xy + y^2) = 7(2x+y)^2
2) (x-4)^2 - 9(x+3)^2 = (x-4+3x+9)(x-4-3x-9) = -(4x+5)(2x-13)
3) 10(x+5)^2 - 19(x+5) + 6 = (2(x+5)-3)(5(x+5)-2) = (2x+7)(5x+23)
4) a. 16a^4 - b^2 = (4a^2+b)(4a^2-b)
b.16(x-1)^4 - (x^2 - 1)^2 = (4(x-1)^2+(x^2-1))(4(x-1)^2-(x^2-1)) = (5x^2-8x+3)(3x^2-8x+5)
=(x-1)^2(5x-3)(3x-5)
5) a. a(1-x)(1-2x) + b≡2x^2 + cx - 9
2ax^2-3ax+(a+b) = 2x^2+cx-9
By comparing the coefficient, a = 1, c = -3a = -3, 1+ b = -9 ==> b = -10
b.40 - 4 (x - 1) (2x -1) = -4(-10+(1-x)(1-2x))=-4(2x^2-3x-9) = 4(x-3)(2x-3)
6) a.3x^3 + 1/9 = 3(x^3+ 1/27) = 3(x+1/3)(x^2-x/3+1/9)
b.x^5 y - 125x^2 y^4=x^2*y(x^3-125y^3)=x^2 * y * (x-5y)(x^2 + 5xy + 25y^2)
7) a^10 + 4a^9 - ab^9 - 4b^9 = a^9(a+4)-b^9(a+4) = (a+4)(a^9-b^9)
= (a+4)(a^3-b^3)(a^6+a^3*b^3+b^6) = (a+4)(a-b)(a^2+ab+b^2)(a^6+a^3*b^3+b^6)

1) (14X-7Y) (2X-Y)
2) -(4X+5)(2x+9)