maths! maths! maths!

2009-07-22 9:32 pm

p. 14
2. Factorize the following expressions.
a. a2/64 - 9b2/4
b. 289 - x6y4
c.3x6 - 48x4 + 192x2
d. rx - ry + ty - tx
e. (x+y) (2x-y) -3x-3y
f. (x+y) (2a-3b) + (x+y) (2b-c)
g. 27-x3
h. 16m3

回答 (1)

老爺子

2009-07-22 9:57 pm

✔ 最佳答案

a.
a2/64 - 9b2/4
= (a/8)2 - (3b/2)2
= [(a/8) - (3b/2)][(a/8) + (3b/2)]

b.
289 - x6y4
= (17)2 - (x3y2)
= (17 - x3y2)(17 + x3y2)

c.
3x6 - 48x4 + 192x2
= 3x2(x4 - 16x2 + 64)
= 3x2[(x2)2 - 2(x2)(8) + (8)2]
= 3x2(x2 - 8)2

d.
rx - ry + ty - tx
= r(x - y) + t(y - x)
= r(x - y) - t(x - y)
= (r - t)(x - y)

e.
(x + y)(2x - y) - 3x - 3y
= (x + y)(2x - y) - 3(x + y)
= (x + y)(2x - y - 3)

f.
(x + y)(2a - 3b) + (x + y)(2b - c)
= (x + y)[(2a - 3b) + (2b - c)]
= (x + y)(2a - b - c)

g.
27 - x3
= (3)3 - (x)3
= (x - y)(x2 + xy + y2)

h.
16m3
= 24m3

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