中二因式分解，maths高手進來~!!!!(急~!20點).

1.a^2+4a+4
=a^2+2(a)(2)+2^2
=(a+2)^2
2.4c^2-12c+9
=(2c)^2-2(2c)(3)+3^2
=(2c-3)^2
3.16m^2+8mn+n^2
=(4m)^2+2(4m)(n)+n^2
=(4m+n)^2
4.49s^2+28st+4t^2
=(7s)^2+2(7s)(2t)+(2t)^2
=(7s+2t)^2
5.9b^2-6b+1
=(3b)^2-2(3b)(1)+1^2
=(3b-1)^2
6.25d^2+20d+4
=(5d)^2+2(5d)(2)+2^2
=(5d+2)^2
7.p^2-10pq+25q^2
=p^2-2(p)(5q)+(5q)^2
=(p-5q)^2
8.4x^2-52xy+169y^2
=(2x)^2-2(2x)(13y)+(13y)^2
=(2x-13y)^2
9.x^2+9x+8
=(x+8)(x+1)
10.x^2-3x-10
=(x-5)(x+2)
*Use cross method in 9 and 10

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

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

3.
16m^2+8mn+n^2
=(4m+n)^2

4.
49s^2+28st+4t^2
=(7s+2t)^2

5.
9b^2-6b+1
=(3b-1)^2

6.
25d^2+20d+4
=(5d+2)^2

7.
p^2-10pq+25q^2
=(p-5)^2

8.
4x^2-52xy+169y^2
=(2x-13y)^2

9.
x^2+9x+8
=(x+1)(x+8)

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

1.(a+2)^2
2.(2c-3)^2
3.(4m+n)^2
4.(7s+2t)^2
5.(3b-1)^2
6.(5d+2)^2
7.(p-5q)^2
8.(4x-13y)^2
9.(x+8)(x+1)
10.(x-5)(x+2)

因為(a-b)^2=a^2-2ab+b^2
(a+b)^2=a^2+2ab+b^2
1.a^2+4a+4
=(a+2)^2
2.4c^2-12c+9
=(2c-3)^2
3.16m^2+8mn+n^2
=(4m+n)^2
4.49s^2+28st+4t^2
=(7s+2t)^2
5.9b^2-6b+1
=(3b-1)^2 (注意：1=1^2)
6.25d^2+20d+4
=(5d+2)^2
7.p^2-10pq+25q^2
=(p+5q)^2
8.4x^2-52xy+169y^2
=(2x-13y)^2
9.x^2+9x+8
=x(x+9)+8
10.x^2-3x-10
=x(x-3)-10

2012-10-23 15:59:40 補充：
sorry,
9. should be x^2+9x+8
=(x+1)(x+8)
10. should be x^2-3x-10
=(x+2)(x-5)