F.3數學一問( 簡易多項式的因式分解)

1.
4x2 + 4x + 1
= (2x)2 + 2(2x)(1) + (1)2
= (2x + 1)2


2.
9x2 - 12xy + 4y2
= (3x)2 - 2(3x)(2y) + (2y)2
= (3x - 2y)2


3.
3y2 - 12xy + 12x2
= 3[y2 - 4xy + 4x2]
= 2[(y)2 - 2(y)(2x) + (2x)2]
= 2(y - 2x)2


1.
25 - 10x + x2
= (5)2 - 2(5)(x) + (x)2
= (5 - x)2


2.
9y2 + 1 + 6y
= 9y2 + 6y + 1
= (3y)2 + 2(3y)(1) + (1)2
= (3y + 1)2


3.
3x2 - 30xy + 75y2
= 3[x2 - 10xy + 25y2]
= 3[(x)2 - 2(x)(5y) + (5y)2]
= 3(x - 5y)2


4.
(a-1)2 - 4(a-1) + 4
= (a-1)2 - 2(a-1)(2) + (2)2
= [(a - 1) - 2]2
= (a - 1 - 2)2
= (a - 3)2


5.
16a4 - 72a2b2 + 81b4
= (4a2)2 - 2(4a2)(9b4) + (9b2)2
= [4a2 - 9b2]2
= [(2a)2 - (3b)2]2
= [(2a + 3b)(2a - 3b)]2
= (2a + 3b)2(2a - 3b)2

基礎訓練 (p.7)
1. 4x^2 + 4x + 1
=(2x)^2 + 2(2x)(1) + 1^2 = (2x+1)^2

2. 9x^2 - 12xy + 4y^2
=(3x)^2 - 2(3x)(2y) + (2y)^2 = (3x-2y)^2

3. 3y^2 - 12xy + 12x^2
=3(y^2 - 4xy + 4x^2)=3(y^2 - 2(2x)(y) + (2x)^2) = 3(y-2x)^2


課堂練習 (p.9)
1. 25 - 10x + x2
=5^2 - 2(5)(x) + x^2 = (5-x)^2

2. 9y^2 + 1 + 6y
=(3y)^2 + 1^2 + 2(3y)(1) = (3y+1)^2

3. 3x2 - 30xy + 75y2
=3(x^2 - 10xy + 25y^2) = 3(x^2 - 2(x)(5y) + (5y)^2) = 3(x-5y)^2

4. (a-1)^2 - 4(a-1) + 4
=(a-1)^2 - 2(2)(a-1) + 2^2 = (a-1-2)^2 = (a-3)^2

5. 16a^4 - 72a^2b^2 + 81b4
=(4a^2)^2 - 2(4a^2)(9b^2) + (9b^2)^2 = (4a^2 - 9b^2)^2

2009-05-16 20:25:24 補充：
003 -->基礎訓練 (p.7) Q3 answer is incorrect

answers:
1: (2x+1)^2
2: (3x-2y)^2
3: (z3y - 2z3x)^2

1: (x-5)^2
2: (3y+1)^2
3: (z3x - 5z3 y)^2
4: (a-3)^2
5: (4a^2-9b^2)^2

can't type the syb of root. so I use z instert