[F.3數]Factorization(40分有答案求步驟)

2010-09-08 1:38 am

Factorize the following expressions.

(Example)
2m(3m-8n)-9n(m+n)
=6m^2-25mn-9n^2
=(3m+n)(2m-9n)

(Graph Paper)
　３ｍ｜＋ｎ
　２ｍ｜－９ｎ
－－－－－－－
(2mn)+(-27mn)=-25mn
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(1) 37hk+10(1+3h^2 k^2)

(2) u^2+4uv+3v^2-7u-21v

(3) 15(c+2)^2+11(c+2)(d-3)-4(d-3)^2

Answer:
(1) (5+6hk)(2+5hk)

(2) (u+3v)(u+v-7)

(3) (15c-4d+42)(c+d-1)

更新1:

thank you very much!!!!

回答 (1)

用戶2053

2010-09-08 2:13 am

✔ 最佳答案

1)37hk+10(1+3h^2 k^2)= 30(hk)^2 + 37hk + 10= (5+6hk)(2+5hk)
(Graph Paper)6hk.....|.....55hk.....|.....2
___________________(6hk)2 + (5hk)5 = 37hk
(2) u^2+4uv+3v^2-7u-21v= u^2 + (4v - 7)u + 3v(v - 7)= (u + 3v)(u + v - 7)
(Graph Paper)u...........| .... 3vu...........|.....(v - 7)
____________________
u(v - 7) + 3vu = (4v - 7)u
(3) 15(c+2)^2+11(c+2)(d-3)-4(d-3)^2= [15(c+2) - 4(d-3)] [(c+2) + (d-3)]= (15c + 30 - 4d + 12) (c + d - 1)= (15c - 4d + 42) (c + d - 1)
(Graph Paper)15(c+2).....| -4(d-3)(c+2)....... | (d-3)
____________________________________15(c+2)(d-3) + (-4)(d-3)(c+2) = 11(c+2)(d-3)

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