F. 2 Maths, 十萬火急

1. 4x2+ 4xy + y2
=(2x+y)2

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

3. 16 - 8x + x2
=(x-4)2

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

5. x2y2 - 6xy + 9
(xy-3)2

6. a3 - 64
=(a-4)(a2+4a+16)


7. 27a3 + 125b3
=(3a+5b)(9a2+15ab+25b2)

8. 2a3 -54
=2(a3 -27)
=2(a-3)(a2 -54+3a+9)

9. a6 - b6
=(a2-b2)(a4+a2b2+b4)
=(a+b)(a-b)(a4+a2b2+b4)


10. a2 - b2 -ac + bc
=(a-b)(a+b)-c(a-b)
=(a-b)(a+b-c)

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

12. 2(a + b)2 - 8(a-b)2
=2[(a+b)2 - 4(a-b)2]
=2[(a+b)-2(a-b)][(a+b)+2(a-b)]
=2(-a+3b)(3a-b)
=2(3b-a)(3a-b)

第9題計錯喇...應該係:
a6 - b6
=(a3)2-(b3)2
=(a3+b3)(a3-b3)
=(a+b)(a2-ab+b2)(a-b)(a2+ab+b2)
=(a+b)(a-b)(a2+ab+b2)(a2-ab+b2)

(d數目都係次方)

1. 4x' + 4xy + y'
=4x'+2xy+2xy+y'
=2x(2x+y)+y(2x+y)
=(2x+y)(2x+y)
2. x' - 10x +25
=x'-5x-5x+25
=x(x-5)-5(x-5)
=(x-5)(x-5)
3. 16 - 8x + x'
=16-4x-4x+x'
=4(4-x)-x(4-x)
=(4-x)(4-x)
4. 9x' - 12xy+4y'
=9x'-6xy-6xy+4y'
=3x(3x-2y)-2y(3x-2y)
=(3x-2y)(3x-2y)
5. x'y' - 6xy + 9
=x'y'-3xy-3xy+9
=xy(xy-3)-3(xy-3)
=(xy-3)(xy-3)
6. a" - 64
=a"-4a'+4a'-16a+16a-64
=a'(a-4)+4a(a-4)+16(a-4)
=(a'+4a+16)(a-4)
7. 27a" + 125b"
=27a"-45a'b+45a'b-75ab'+75ab'-125b"
=9a'(3a-5b)+15ab(3a-5b)+25b'(3a-5b)
=(9a'+15ab+25b')(3a-5b)
8. 2a" -54
=2(a"-27)
=2(a"-3a'+3a'-9a+9a-27)
=2(a'(a-3)+3a(a-3)+9(a-3))
=2(a'+3a+9)(a-3)
9. a<6> - b<6>
=a<6>-a<5>b+a<5>b-a<4>b'+a<4>b'-a"b"+a"b"-b<4>a'+b<4>a'-a<5>b+b<5>a-b<6>
=a<5>(a-b)+a<4>b(a-b)+a"b'(a-b)+a'b"(a-b)+ab<4>(a-b)+b<5>(a-b)
=(a<5>+a<4>b+a"b'+a'b"+ab<4>+b<5>)(a-b)
10. a' - b' -ac + bc
=a(a-c)-b(b-c)
=(a-b)(b-c)
11. (a - b) " - a + b
=(a-b)"-(a-b)
=((a-b)'-1)(a-b)
=(a'-ab-ab+b'-1)(a-b)
=(a'-2ab+b'-1)(a-b)
12. 2(a + b)' - 8(a-b)'
=2(a'+ab+ab+b'-4a'+4ab+4ab-4b')
=2(-3a'+10ab-3b')