F.3 因式分解~~20分!!!!!!

1) (a-12)^2 + 5b(12-a)

(a - 12)^2 + 5b(12 - a)

=(a - 12)^2 +[-5b(a - 12)]----------------------------抽負

=(a - 12)^2 - 5b(a - 12)-------------------------------負正得正

=(a - 12)[(a - 12) - 5b)]-------------------------------抽因子(a-12)

=(a - 12)(a - 5b - 12)---------------------------------排好+答案

驗算:

(a - 12)(a - 5b - 12)

=(a-12)^2+5b(12-a)

SO,the answer is right.

2)2m²-8m+8

2m²-8m+8

=2(m² - 4m + 4)---------------------------------------抽因子(2)

=2(m - 2)(m - 2)-----------------------------------------用十字相乘法:

m↘-2
m↗-2
-------------------
-2m-2m=-4m

=2(m - 2)²-----------------------------------------------(m-2)(m-2)=(m-2)² e.g a*a=a²≠2a(answer)

驗算:

2(m-2)²

=(2)(m-2)(m-2)

=(2)(m²-4m+4)

=2m²-4m+4

SO ,the aswer is right.

3)
5m² + 45 + 30m

=5(m²+9+6m)-----------------------------抽因子(5)

=5(m²+6m+9)-----------------------------排列好,以便進行十字相乘

m↘3
m↗3
-------------------
3m+3m=6m

=5(m + 3)(m + 3)------------------------十字相乘

=5(m + 3)²--------------------------------答案

驗算:

5(m+3)²

=5(m+3)(m+3)

=5m+15(m+3)

=5m²+45+30m

SO,the answer is right.

4)2a^4+9a²+8a²b+ 36b

2a^4+9a^2+8a²b+36b

=[2a^4+9a^2]+[8a²b+36b]--------------排列好

=a²(2a²+9)+b(8a²+36)------------------抽因子a²(2a²+9),(b)

=a²(2a²+9)+4b(2a²+9)--------------------抽因子4

=(2a²+9)(a²+4b)----------------------------抽因子(2a²+9),答案

驗算:

(2a²+9)(a²+4b)

=a²(2a²+9)+4b(2a²+9)

=a²(2a²+9)+b(8a²+36)

=[2a^4+9a^2]+[8a²b+36b]

=2a^4+9a²+8a²b+36b

SO,the answer is right.


5)56ax+4b²+32bx+7ab

56ax+4b²+32bx+ 7ab

=56ax+32bx+4b²+7ab-------------------排列法

=x(56a+32b)+b(7a+4b)------------------在各項裹抽出因子, x 和 b

=8x(7a+4b)+b(7a+4b)--------------------抽出因子8

=(8x+b)(7a+4b)-----------------------------抽出因子(7a+4b),answer

驗算:

(8x+b)(7a+4b)

=8x(7a+4b)+b(7a+4b)

=x(56a+32b)+b(7a+4b)

=56ax+32bx+4b²+7ab

56ax+4b²+32bx+ 7ab

So,the answer is right.

6)24by-3ax+2bx-36ay

24by-3ax+2bx-36ay

=24by-36ay+3ax+2bx---------------------------排列法

=y(24b-36a)+x(2b-3a)---------------------------在各項中因式分解

=12y(2b-3a)+x(2b-3a)---------------------抽因子12

=(x+12y)(2b-3a)-----------------------------抽因子(2b+3a)+answer

驗算:

(x+12y)(2b-3a)

=12y(2b-3a)+x(2b-3a)

=y(24b-36a)+x(2b-3a)

=24by-36ay+3ax+2bx

=24by-3ax+2bx-36ay

7)(16x²-24xy+ 9y²)+8(4x-3y)+16

(16x²+9y²-24xy)-4(4x²+28x+49)------------------展開

=(16x²-24xy+9y²)-4(4x²+28x+49)----------------排好,以便進行因式分解

4x↘-3x　　　　2x↘7
4x↗-3x　　　　2x↗7
-------------　　　---------------------
-12x-12x=-24x　14x+14x=28x

=(4x-3y)²-4(2x+7)²-----------------十字相乘

=(4x-3y)²-(2²)(2x+7)²-------------將4因式分解

=(4x-3y)²-(2(2x + 7))²-----------拼項

=(4x-3y)²-(4x + 14)²-------------拼合

設a=4x-3y,b=4x+14--------------------------這樣會比較易計

(4x-3y)²-(4x + 14)²

=a²- b²

=(a+b)(a-b)

把a和b還原成4x-3y和4x+14,

=[(4x-3y)+(4x+14)][(4x-3y)-(4x + 14)]

=(8x-3y+14)(-3y-14)-------------------------------拼項+answer

驗算:

(8x-3y+14)(-3y-14)

=(4x-3y)+(4x+14)][(4x-3y)-(4x + 14)]

=(16x²+9y²-24xy)-4(4x²+28x+49)

so,the answer is right.


8)(16x²-24xy+9y²)+8(4x-3y)+16

(16x²-24xy+9y²)+8(4x-3y)+16

=(4x-3y)²+8(4x-3y)+16-------------------------因式分解

設a為4x-3y

=a²+8a+16

=(a+4)²

還原a至4x-3y.

=[(4x-3y)+4]²

=(4x-3y+4)²-----------------------拼合+answer

驗算:

(4x-3y+4)²

=[(4x-3y)+4]²

=(4x-3y)²+8(4x-3y)+16

=(16x²-24xy+9y²)+8(4x-3y)+16

so,the answer is true

注意事項:

一)有些題目是要先展開,後因解

二)a*a=a²≠2a

嘩! 你真係打得好詳細
抵你攞最佳回答

1)
(a - 12)^2 + 5b(12 - a)
=(a - 12)^2 + 5b(a - 12) ( - 1)
=(a - 12)^2 - 5b(a - 12)
=(a - 12) ((a - 12) - 5b)
=(a - 12) (a - 5b - 12)


2)
2m^2 - 8m + 8
=2(m^2 - 4m + 4)
=2(m - 2) (m - 2)
=2(m - 2)^2


3)
5m^2 + 45 + 30m
=5m^2 + 30m + 45
=5(m^2 + 6m + 9)
=5(m + 3) (m + 3)
=5(m + 3)^2


4)
2a^4 + 9a^2 + 8a^(2)b + 36b
=a^2(2a^2 + 9) + b(8a^2 + 36)
=a^2(2a^2 + 9) + 4b(2a^2 + 9)
=(2a^2 + 9) (a^2 + 4b)


5)
56ax + 4b^2 + 32bx + 7ab
=x(56a + 32b) + b(7a + 4b)
=8x(7a + 4b) + b(7a + 4b)
=(8x + b) (7a + 4b)


6)
24by - 3ax + 2bx - 36ay
=y(24b - 36a) + x(2b - 3a)
=12y(2b - 3a) + x(2b - 3a)
=(x + 12y) (2b - 3a)


7)
(16x^2 + 9y^2 - 24xy) - 4(4x^2 + 28x + 49)
=(16x^2 - 24xy + 9y^2) - 4(4x^2 + 28x + 49)
=(4x - 3y)^2 - 4(2x + 7)^2
=(4x - 3y)^2 - (2^2) (2x + 7)^2
=(4x - 3y)^2 - (2(2x + 7))^2
=(4x - 3y)^2 - (4x + 14)^2

Let a=4x - 3y b=4x + 14

=a^2 - b^2
=(a + b) (a - b)

Sub. a & b

=((4x - 3y) + (4x + 14)) ((4x - 3y) - (4x + 14))
=(8x - 3y + 14) ( - 3y - 14)

If you want to make it look BETTER - - > = - (8x - 3y + 14) (3y + 14)


8)
(16x^2 - 24xy + 9y^2) + 8(4x - 3y) + 16
=(4x - 3y)^2 + 8(4x - 3y) + 16

Let a=4x - 3y

=a^2 + 8a + 16
=(a + 4)^2

Sub. a

=((4x - 3y) + 4)^2
=(4x - 3y + 4)^2

2007-11-01 20:09:48 補充：
上面位高手嘅第二條答案好似有啲問題…希望我嘅無問題，啱您用啦！

1) (a-12)^2 + 5b(12-a)
=(a-12)^2-5b(a-12)
=(a-12)(a-12-5b)

2) 2m^2 - 8m +8
=(m+2)(2m+4)<---用 cross method

3) 5m^2 + 45 +30m
=5m^2+30m+45
=5(m^2+6m+9)
=5(m+3)(m+3)
=5(m+3)^2

4)2a^4 + 9a^2 + 8a^(2)b + 36b
=a^2(2a^2+9)+4b(2a^2+9)
=(a^2+4b)(2a^2+9)

5) 56ax + 4b^2 + 32bx + 7ab
=56ax+32bx+4b^2+7ab
=8x(7a+4b)+b(4b+7a)
=(8x+b)(7a+4b)

6) 24by - 3ax + 2bx - 36ay
=24by+2bx-3ax-36ay
=2b(12y+x)-3a(x+12y)
=(2b-3a)(12y+x)

7)(16x^2 + 9y^2 - 24xy) - 4(4x^2 + 28x +49)
=(16x^2 - 24xy+ 9y^2) - 4(4x^2 + 28x +49)
=(4x-3y)^2-4(2x+7)^2
=(4x-3y)^2-[2(2x+7)]^2
=(4x-3y-4x-14)(4x-3y+4x+14)<---將(4x-3y)代成a，2(2x+7)代成 b，變左a^2-b^2，計完之後將(4x-3y)代入去a，2(2x+7)代入去 b
=(-3y-14)(8x-3y+14)

8) (16x^2 - 24xy + 9y^2) + 8(4x-3y) + 16
=(4x-3y)^2+8(4x-3y)+16
=(4x-3y+4)(4x-3y+4)<---將(4x-3y)當成x，就會係 x^2+8x+16，用 cross method 計完之後再用番(4x-3y+4)代番去 x
=(4x-3y+4)^2

2007-11-02 22:45:32 補充：
感謝下面嗰位，第 2 題的確有 d 問題 ^^"2) 2m^2 - 8m +8=(m-2)(2m-4)<---用 cross method=2(m-2)(m-2)<---係(2m+4)再抽個 2 出黎=2(m-2)^2或2m^2 - 8m +8=2(m^2-4m+4)=2(m-2)^2 <---直接用(a-b)^2=a^2-2ab+b^2 呢條 identity