中二數學問題 (20 分) !!~~ 急急急 ~~

1.k^2 + 16k + 64
=k^2 +2(8)k + 8^2
=(k + 2) ^ 2

2.c^2 - 6c + 9
=c^2 - 2(3)c + 3^2
=(c - 3)^2

3.t^2 - 14t + 49
=t^2 - 2(7)t + 7^2
=(t-7)^2

4.z^2 + 20yz + 100y^2
=z^2 + 2(10y)z + (10y)^2
=(z+10y)^2

5.12m^2 + 12m + 3
=3[(2m)^2 + 2(2m)1 + 1^2]
=3(2m+1)^2

6.80r ^2 + 40rs + 5s^2
=5[(4r) ^2 + 2(4r)s + s^2]
=5(4r+s)^2

7.(c - d)^2 + 4(c - d) + 4
=(c - d)^2 + 2(c - d)2 + 2^2
=[(c - d)+2]^2
=(c - d+2)^2

8.1 - 6t^2 + 9t^4 - 121s^2
=(9t^4- 6t^2+1) - 121s^2
=[(3t^2)^2-2(3t^2)1+1^2]-(11s)^2
=(3t^2-1)^2-(11s)^2
=[(3t^2-1)-(11s)][(3t^2-1)+(11s)]
=(3t^2-11s-1)(3t^2+11s-1)

9.w^4 + 18w^2x^2 + 81x^4
=(w^2)^2 + 2(w^2)(9x^2) + (9x^2)^2
=[w^2 + (3x)^2]^2

1.k^2 + 16k + 64
=(k+8)^2


2.c^2 - 6c + 9
=(c-3)^2

3.t^2 - 14t + 49
=(t-7)^2

4.z^2 + 20yz + 100y^2
=(z+10)^2

5.12m^2 + 12m + 3
=3(4m^2+4m+1)
=3(2m+1)^2

6.80r ^2 + 40rs + 5s^2
=5(16r^2+8rs+s^2)
=5(4r+s)^2

7.(c - d)^2 + 4(c - d) + 4
=[(c-d)+4)]^2
=(c-d+4)^2

9. w^4 + 18w^2x^2 + 81x^4
=(w^2+9x^2)^2

2007-10-23 19:43:45 補充：
8.1 - 6t^2 + 9t^4 - 121s^2=(9t^4- 6t^2+1) - 121s^2=[(3t^2)^2-2(3t^2)1+1^2]-(11s)^2=(3t^2-1)^2-(11s)^2=[(3t^2-1)-(11s)][(3t^2-1)+(11s)]=(3t^2-11s-1)(3t^2+11s-1)