f3 mth questions!!!急~聽日要交!

2010-10-18 8:58 am

factorize the following expressions.

22.75(c - 3d)^2 - 27(2c - 5d)^2
ANS : 3c(30d - 11c)

31.x^4 - 10x^2 + 9
ANS : (x + 3)(x - 3)(x +1)(x - 1)

32.64r^3 - 343
ANS : (4r - 7)(16r^2 + 28r +49)

35(a) Factorize 4a^2 - 4ab + b^2
ANS : (2a - b)^2

(b)Use the reslt in (a) to factorize 4a^2- 4ab +b^2 - c^2.
ANS : (2a - b + c)(2a - b - c)

36.(a) Factorize m^2 + 6m + 9
ANS : (m + 3)^2

(b)Use the reslt in (a) to factorize x^2 + 2xy + y^2 + 6(x + y) + 9.
ANS : (x + y + 3)^2

求step,thx~~
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一定要有完整啲step~~唔好亂做,要同個ans一樣,一定要岩同埋要清楚(要睇得明你寫咩)!!!!thx~~~

回答 (1)

用戶26240

2010-10-18 9:43 am

✔ 最佳答案

22.
75(c - 3d)² - 27(2c - 5d)²
= 75(c² - 6cd + 9d²) - 27(4c² - 20cd + 25d²)
= 75c² - 450cd + 675d² - 108c² + 540cd - 675d²
= 90cd -33c²
= 3c(30d - 11c)

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31.
Let y = x²
Then x⁴ - 10x² + 9
= y² - 10y + 9
= (y - 9)(y - 1)
= (x² - 3²)(x² - 1²)
= (x + 3)(x - 3)(x + 1)(x - 1)

=====
32.
Let u = 4r
64r³ - 343
= (4r)³ - 7³
= u³ - 7³
= (u - 7)(u² + 7u + 7²)
= [(4r) - 7] [(4r)² + 7(4r) + 7²]
= (4r - 7)(16r² + 28r + 49)

=====
35.(a)
Let u = 4a
Then 4a² - 4ab + b²
= (2a)² - 2(2a)b + b²
= u² - 2ub + b²
= (u - b)²
= [(2a) - b]²
= (2a - b)²

35.(b)
Let v = (2a - b)
Then 4a² - 4ab + b² - c²
= (4a² - 4ab + b²) - c²
= (2a - b)² - c²
= v² - c²
= (v + c)(v - c)
= (2a + b + c)(2a + b - c)

=====
36.(a)
m² + 6m + 9
= (m)² + 2(m)(3) + (3)²
= [(m) + (3)]²
= (m + 3)²

36.(b)
Let m = x + y
Then x² + 2xy + y² + 6(x + y) + 9
= (x + y)² + 6(x + y) + 9
= m² + 6m + 9
= (m + 3)²
= (x + y + 3)²

參考: 土扁

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