[急問20點] 中二數學題 恆等式/因式分解 唔該幫幫手丫

1. 4n^2 + 20n + 25
= (2n)^2 + 2(2n)(5) + 5^2
= (2n + 5)^2

2. 2y^2 - 28y + 98
= 2(y^2 - 14y + 49)
= 2(y^2 - 2(2y)(7) + 7^2)
= 2(y - 7)^2

3. y^2 - 3y - 10
= (y - 5)(y + 2)

4. 2a^2 - 5a - 3
= (2a + 1)(a - 3)

5. 6m^2 - 11m + 4
= (3m - 4)(2m - 1)

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

6b. 2a^2 - ab - b^2 - a + b
= (2a + b)(a - b) - a + b
= (2a + b)(a - b) - (a - b)
= (2a + b - 1)(a - b)

7. (3x + 6y) (-x + 2y)
= 3(x + 2y)(2y - x)
[如果您想做展開, 會變做
3(x + 2y)(2y - x)
= 3(2y + x)(2y - x)
= 3(4y^2 - x^2)
= 12y^2 - 3x^2, 但我唔係好知您想問咩... 唔好意思]

8. a^2 - (b - c)^2
= (a + b - c)(a - (b - c))
= (a + b - c)(a - b + c)

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

10. x^3 - 27y^3
= x^3 - (3y)^3
= (x - 3y)(x^2 + x(3y) + (3y)^2)
= (x - 3y)(x^2 + 3xy + 9y^2)

11. 8a^3 + 1
= (2a)^3 + 1^3
= (2a + 1)((2a)^2 - 2a(1) + 1)
= (2a + 1)(4a^2 - 2a + 1)

12. x^5 - x^3
= x^3(x^2 - 1)
= x^3(x^2 - 1^2)
= x^3(x + 1)(x - 1)

其實您d題目應該全部都係因式分解? 我完全見唔到恆等式ge題目, 定您會唔會打漏左d野? 另外, 第2, 3, 4, 5, 6a, 9題都係好似平時咁用交叉個方法去撞d數, 所以冇step的, 有咩可以再問啊!

2012-10-09 00:53:58 補充：
小心樓上兩位的答案均有少許錯誤, 謝謝!

1 .
4n^2+20n+25
=(2n+5)^2

2 .
2y^2-28y+98
=2(y^2-14+49)
=2(y-7)^2

3 .
y^2-3y-10
=(y-5)(y+2)

4 .
2a^2-5a-3
=(a-3)(2a+1)

5 .
6m^2-11m+4
=(3m-4)(2m-1)

6 a)
2a^2-ab-b^2
=(a-b)(2a+1)

6 b)
2a^2-ab-b^2-a+b
=(a-b)(2a+1)-(a-b)
=(a-b)(2a+1-1)
=2a(a-b)

7 .
(3x+6y) (-x+2y)
=-3x^2+6xy-6xy+12y^2
=-3x^2+12y^2
=-3(x^2-4y^2)
=-3(x+2y)(x-2y)

8 .
a^2-(b-c)^2
=(a-b+c)(a+b-c)

9 .
4x^2+xy-3y^2
=(4x-3)(x+1)

10
x^3-27y^3
=(x-3y)(x^2+3xy+9y^2)

11
8a^3+1
=(2a+1)(4a^2-2a+1)

12
x^5-x^3
=x^3(x^2-1)
=x^3(x-1)(x+1)

講明唔知對不對
1.4n^2+20n+25
=(2n+5)^2
n=-5/2 or n=-5/2

2.2y^2-28y+98
=(y-7)^2
y=7 or y=7

3.y^2-3y-10
=(y+2)(y-5)
y=-2 or y=5

4.2a^2-5a-3
=(2a+1)(a-3)
a=-1/2 or a=3

5.6m^2-11m+4
=(2m-1)(3m-4)
m=1/2 or m=4/3

6a. 2a^2-ab-b^2
(2a+b)(a-b)=0

由(a)可得
b.2a^2-ab-b^2-a+b
=(2a+b)(a-b)-a+b
=(2a+b)(a-b)-(a-b)
=(a-b)(2a+b-1)

7.(3x+6y)(-x+2y)
=-3x^2+12y^2
=-3(x^2-4y^2)
=-3[x^2-(2y)^2]
=-3(x+2y)(x-2y)

8.a^2-(b-c)^2=(a+b-c)(a+b+c)

9.4x^2+xy-3y^2
=(x+y)(4x-3y)

10.x^3-27y^3
=x^3-(3y)^3
=(x-3y)[(x^2+3xy+(3y)^2]
=(x-3y)(x^2+3xy+9y^2)

11.8a^3+1
=(2a)^3+1^3
=(2a-1)[(2a)^2+2a+1^2]
=(2a-1)(4a^2+2a+1)

12.x^5-x^3
=x^3(x^2-1^2)
=x^3(x+1)(x-1)

1 . 4n^2+20n+25=(2n+5)^2

2 . 2y^2-28y+98=2(y^2-14y+49)=(y-7)^2

3 . y^2-3y-10=(y-5)(y+2)

4 . 2a^2-5a-3=(2a+1)(a-3)

5 . 6m^2-11m+4=(3m-4)(2m-1)

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

b) 2a^2-ab-b^2-a+b=唔識

恆等式 ~

7 . (3x+6y) (-x+2y)=-3x^2+12y^2=-3(x^2-4y^2)=-3(x-2y)^2

8 . a^2-(b-c)^2=a^2-b^2-2bc+c^2

9 . 4x^2+xy-3y^2=是恆等式

10 x^3-27y^3=(x-27y)^3

11 8a^3+1=(8a+1)^3

因式分解
12 x^5-x^3=11x^2