数学 Polynomials

1. 32ax^2-50ay^2
=2(16ax^2-25ay^2)
=2a(16x^2-25y^2)
=2a[(4x)^2-(5y)^2]
=2a(4x+5y)(4x-5y)

2.(x+1)^2-81
=(x+1)^2-9^2
=(x+1+9)(x+1-9)
=(x+10)(x-8)

3.121-(2y+3)^2
=11^2-(2y+3)^2
=[11+(2y+3)][11-(2y+3)]
=(11+2y+3)(11-2y-3)
=(14+2y)(8-2y)
=2(7+y)(8-2y)
=4(7+y)(4-y)

4.(3a-7)^2-(2a+5)^2
=[(3a-7)+(2a+5)][(3a-7)-(2a+5)]
=(3a-7+2a+5)(3a-7-2a-5)
=(5a+2)(a-12)

2012-12-09 16:32:56 補充：
前兩位第3題係做錯既。

2012-12-09 16:35:32 補充：
佢地根本未factor哂,仲有1個公因數2可以抽出黎。

1)32ax²-50ay²
=2a(16x²-25y²)
=2a(4x+5y)(4x-5y)

2)(x+1)²-81
=(x+1)²-9²
=(x+1+9)(x+1-9)
=(x+10)(x-8)

3)121-(2y+3)²
=11²-(2y+3)²
=(11+2y+3)(11-2y-3)
=(2y+14)(-2y+8)

4)(3a-7)²-(2a+5)²
=[(3a-7)+(2a+5)][(3a-7)-(2a+5)]
=(5a-2)(a-12)

2012-12-09 16:48:33 補充：
3)121-(2y+3)²
=11²-(2y+3)²
=(11+2y+3)(11-2y-3)
=(2y+14)(-2y+8)
=2(y+7)2(-y+4)
=4(y+7)(-y+4)

感謝LUNG.提點
我的確大意唔記得要take common factor

Q1. 32ax^2-50ay^2
=2a(16x^2-25y^2)
=2a [ (4x)^2 - (5y)^2 ]
=2a (4x+5y) (4x-5y)

2012-12-09 16:29:16 補充：
Q2. (x+1)^2-81
=(x+1)^2 - (9)^2
=[ (x+1+9) (x+1-9) ]
=(x+10) (x-8)

Q3. 121-(2y+3)^2
=(11)^2 - (2y+3)^2
=(11-2y-3) (11+2y+3)
=(8-2y) (14+2y)

Q4. (3a-7)^2-(2a+5)^2
=[ (3a-7)-(2a+5)] [ (3a-7)+(2a+5)]
=(a-12) (5a-2)