Maths......好趕架

Expand the following expression.

1. (2y-x)(x-2y)
= -(x-2y)(x-2y)
= -(x-2y)^2
= -[x^2 - 2(x)(2y) + (2y)^2]
= -(x^2 - 4xy + 4y^2)
= -x^2 + 4xy - 4y^2
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Factorize the following expression.
1. 8a(m-2n) - 12b(2n-m)
= 8a(m-2n) + 12b(m-2n)
= (8a + 12b)(m-2n)
= 4(2a + 3b)(m - 2n)
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2. (3x-y)(x-y)+y(y-x)
= (3x-y)(x-y) - y(x-y)
= [(3x-y) - y] (x-y)
= (3x-y - y) (x-y)
= (3x - 2y) (x-y)
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3. 20x^2 y - 8x^2 y^2 - 10xy^2 + 16x^3 y
= 20x^2 y - 10xy^2 + 16x^3 y - 8x^2 y^2
= 10(2x - y)xy + 8(2x - y) x^2 y
= [ 10xy + 8 x^2 y] (2x - y)
= [ 10 + 8 x] (2x - y)xy
= 2(5 + 4x) (2x - y)xy
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Factorize the following expression.
1. 4x^2 - y^2
= (2x)^2 - y^2
= (2x - y)(2x + y)
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2. 4(x+y)^2 - 4(x+y) + 1
4z^2 - 4z + 1
= (2z)^2 - 2(2z)(1) + 1
= (2z - 1)^2
put z = x+y
4(x+y)^2 - 4(x+y) + 1
= (2(x+y) - 1)^2
= (2x + 2y - 1)^2
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3. (3x+5)^2 - (2x+1)^2
= [ (3x+5) - (2x+1) ] [ (3x+5) + (2x+1) ]
= (3x + 5 - 2x - 1) (3x + 5 + 2x + 1)
= (x + 4) (5x + 6)
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2007-10-25 22:40:05 補充：
我估我做得清楚齊整一 d,唔該投我一票啦

1. (2y-x)(x-2y) = -(x-2y)(x-2y) = -(x-2y)^2 = -(x^2 - 4xy + 4y^2) = -x^2 +4xy-4y^2

Factorize the following expression.
1. 8a(m-2n)-12b(2n-m) =8a(m-2n)+12b(m-2n) = (m-2n)(8a+12b) = 4(m-2n)(2x+3b)

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

3. 20x二次y-8x二次y二次-10xy二次+16x三次y = 20x^2y-10xy^2 - 8x^2y^2 + 16x^3y = 10xy(2x-y) -8x^2y(y-2x) = 10xy(2x-y)+8x^2y(2x-y)
=(2x-y)(10xy-8x^2y) = 2xy(2x-y)(5-4x)

Factorize the following expression.Use : (a+b)(a-b)≣a二次-b二次 ，(a+b)二次)≣a二次+2ab+b二次 ，(a-b)二次≣a二次-2ab+b二次

1. 4x二次-y二次 = (2x)^2 - y^2 - (2x+y)(2x-y)

2. 4(x+y)二次-4(x+y)+1 = [2(x+y)]^2 -2[2(x+y)](1) + 1^2 = (2(x+y)+1)^2 = (2x+2y+1)^2

3. (3x+5)二次-(2x+1)二次 = (3x+5+2x+1)(3x+5-2x-1) = (5x+6)(x+4)