因式分解20分(急)

1.27a^2-12b^2=3(9a^2-4b^2)=3[(3a)^2-(2b)^2]=3(3a+2b)(3a-2b)
7.125r^3+216=(5r)^3+6^3=(5r+6)(25r^2-30r+36)

1. 27a^2-12b^2
27a^2-12b^2
=3(9a^2-4b^2)
=3(3a-2b)(3a+2b)

2. 18(4p-3q)^2 - 8(5p-2q)^2
18(4p-3q)^2 - 8(5p-2q)^2
=2[9(4p-3q)^2 - 4(5p-2q)^2]
=2[3(4p-3q)+2(5p-2q)][3(4p-3q)-2(5p-2q)]
=2(22p-13q)(2p-5q)

3. 8a^2-8ab^2+2b^4
8a^2-8ab^2+2b^4
=2(4a^2-4ab^2+b^4)
=2(2a-b^2)^2

4. x^3y-10x^2y^2+25xy^3
x^3y-10x^2y^2+25xy^3
=xy(x^2-10xy+25y^2)
=xy(x-5y)^2

5. 88a^2-35b^2-ab
88a^2-35b^2-ab
=88a^2-ab-35b^2
=(11a-7b)(8a+5b)

6. (a+b)^2-3(ab+b^2)
(a+b)^2-3(ab+b^2)
=a^2+2ab+b^2-3ab-3b^2
=a^2-ab-b^2
=(a+b)(a-2b)

7. 125r^3+216
125r^3+216
=(5r)^3+6^3
=(5r+6)(25r^2-30r+36)

8. (x-y)^3-(x+y)^3
(x-y)^3-(x+y)^3
=[(x-y)-(x+y)][(x-y)^2+(x-y)(x+y)+(x+y)^2]
=(-2y)[(x^2-2xy+y^2)+(x^2-y^2)+(x^2+2xy+y^2)]
=(-2y)(3x^2+y^2)

9.(a) 分解144x^2+120xy+25y^2為因式
144x^2+120xy+25y^2
=(12x+5y)^2

(b) 從而，將 72/5a^2+12ab+5/2b^2 分解為因式
72/5a^2+12ab+5/2b^2
=[(6p/q)a+(q/p)b]^2................p=2開根號=2^0.5 q=5開根號=5^0.5

10(a) 分解x^2-13x+36為因式
x^2-13x+36
=(x-9)(x-4)

(b) 由此，利用設y=1/x^2，將1/x^4-13/x^2+36 分解為因式
設y=1/x^2
1/x^4-13/x^2+36
=y^2-13y+36
=(y-9)(y-4)

11. 若x^2+cx+12能分解為因式，寫出c的四個可能值
(1) (x+1)(x+12)=x^2+13x+12 所以c=13
(2) (x-1)(x-12)=x^2-13x+12 所以c=-13
(3) (x+2)(x+6)=x^2+7x+12 所以c=7
(4) (x-3)(x-4)=x^2-7x+12 所以c=-7