6.
49a2 - 64
= (7a)2 - 82
=(7a+8)(7a-8)
8.
4h2 - 121k2
=(2h)2 - (11k)2
=(2h+11k)(2h-11k)
10.
-144+c2d2
=c2d2-144
= (cd)2-122
=(cd+12)(cd-12)
12.
-p2q2+r4
=r4-p2q2
= (r2)2 - (pq)2
=(r2+pq)(r2-pq)
14.
f2-25g2h2
=(f)2-(5gh)2
=(f+5gh)(f-5gh)
16.
-100s2+81t2
=81t2-100s2
=(9t)2-(10s)2
=(9t+10s)(9t-10s)
18.
169-(m+7n)2
=132-(m+7n)2
=[13+(m+7n)][13-(m+7n)]
=(13+m+7n)(13-m-7n)
20
(3x+y)2-(z-2)2
= [(3x+y)+(z-2)] [(3x+y)-(z-2)]
=(3x+y+z-2)(3x+y-z+2)
22.
6-54u2
=6(1-9u2)
=6(12-9u2) <---- 1=12=1
=6(1+3u)(1-3u)
24.
28(x+y)2-7(x-y)2 <-抽7出來
=7[4(x+y)2-(x-y)2] <----- 4->22
=7[22(x+y)2-(x-y)2] <-----22(x+y)2 可以抽 2 -->(2(x+y))2
=7[ (2(x+y))2-(x-y)2] <---- (2(x+y))->a (x-y)->b 用恆等式
=7[2(x+y)+(x-y)][2(x+y)-(x-y)] <--拆()
=7(2x+2y+x-y)(2x+2y-x+y)
=7(3x+y)(x+3y)
26.
4c2-9d2-2c-3d
=(2c)2-(3d)2 -2c-3d
=(2c+3d)(2c-3d)- (2c +3d) <--- 後面個舊 -2c-3d 可以抽個負出來 變做 -(2c+3d)
=(2c+3d)(2c-3d-1)
28.
k4-81
(k2)2-92
=(k2+9)(k2-9)
=(k2+9)(k2-32)
=(k2+9)(k+3)(k-3)
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