2條因式分解

1) (4x+5)(4x^2-3)-4x-5
　(4x+5)(4x^2-3)-4x-5
=(4x+5)(4x^2-3)-(4x+5)-----抽"-"出黎
=(4x+5)(4x^2-3-1)-----抽(4x+5)出黎
=(4x+5)(4x^2-4)-----加減數
=4(x^2-1)(4x+5)-----4x^2-4抽4
=4(x+1)(x-1)(4x+5)-----x^2-y^2=(x+y)(x-y)
2) 8(c+2d)^2-50(3c-d)^2
　8(c+2d)^2-50(3c-d)^2
=2[4(c+2d)^2-25(3c-d)^2]-----見到可以抽就抽，抽2出黎
=2{[2(c+2d)]^2-[5(3c-d)]^2}-----4同25可開方，開方後剛好是a^2-b^2
=2[2(c+2d)+5(3c-d)][2(c+2d)-5(3c-d)]------a^2-b^2=(a+b)(a-b)
=2(2c+4d+15c-5d)(2c+4d-15c+5d)-----拆括弧
=2(17c-d)(9d-13c)-----加減數
***將2(c+2d)看作a，5(3c-d)看作b
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＊＊＊因式分解不能乘開

1) (4x+5)(4x^2-3)-(4x+5)
=(4x+5)(4x^2-3-1)
=4(4x+5)(x^2-1)
=4(4x+5)(x+1)(x-1)

2) 2[4(c+2d)^2-25(3c-d)^2]
=2[2^2(c+2d)^2-5^2(3c-d)^2]
=2[(2c+4d)^2-(15-5d)^2]
=2[2c+4d-(15-5d)][2c+4d+15-5d]
=2(2c+9d-15)(2c-d+15)

1. (4x + 5)(4x2 - 3) – 4x – 5
= (4x + 5)(4x2 - 3) – (4x + 5)
= (4x + 5)[(4x2 - 3) - 1]
= (4x + 5)(4x2 - 4)
= 4(4x + 5)(x2 - 1)
= 4(4x + 5)(x + 1)(x - 1)


2. 8(c + 2d)2 – 50(3c - d)2
= 8(c2 + 4cd + 4d2) – 50(9c2 – 6cd + d2)
= 8c2 + 32cd + 32d2 – 450c2 + 300cd – 50d2
= -442c2 + 332cd – 18d2
= -2(221c2 – 166cd + 9d2)

1. (4x + 5)(4x2 - 3) – 4x – 5

= (4x + 5)(4x2 - 3) – (4x + 5)

= (4x + 5)[(4x2 - 3) - 1]

= (4x + 5)(4x2 - 4)

= 4(4x + 5)(x2 - 1)

= 4(4x + 5)(x + 1)(x - 1)


2. 8(c + 2d)2 – 50(3c - d)2

= 8(c2 + 4cd + 4d2) – 50(9c2 – 6cd + d2)

= 8c2 + 32cd + 32d2 – 450c2 + 300cd – 50d2

= -442c2 + 332cd – 18d2

= -2(221c2 – 166cd + 9d2)