因式分解........急........急.....我不明白當中的過程

Q1) (n－4y) ²－16(n－y) ²= 3n(8y－5n)

證明: 左方 = (n－4y) ²－16(n－y) ²

..................= (n-4y)^2 - [4(n-y)]^2

..................= [(n-4y)-4(n-y)] [(n-4y)+4(n-y)]

..................= (n-4y-4n+4y)(n-4y+4n-4y)

..................= (-3n)(5n-8y)

..................= 3n(8y-5n) = 右方

因此, (n－4y) ²－16(n－y) ²= 3n(8y－5n)



Q2) 4(c+2d)²－25(3c－d)²=(17c－d)(9d－13c)

證明: 左方 = 4(c+2d)²－25(3c－d)²

..................= [2(c+2d)]^2 - [5(3c-d)]^2

..................= [2(c+2d)-5(3c-d)] [2(c+2d)+5(3c-d)]

..................= (2c+4d-15c+5d)(2c+4d+15c-5d)

..................= (-13c+9d)(17c-d)

..................= (17c-d)(9d-13c) = 右方

因此, 4(c+2d)²－25(3c－d)²=(17c－d)(9d－13c)

1 . (n－4y) ²－16(n－y) ²= 3n(8y－5n)

ProveL.H.S. = (n－4y) ²－16(n－y) ²

= (n-4y)^2 - [4(n-y)]^2

= [(n-4y)-4(n-y)] [(n-4y)+4(n-y)]

= (n-4y-4n+4y)(n-4y+4n-4y)

= (-3n)(5n-8y)

= 3n(8y-5n)

= R.H.S.

So , (n－4y) ²－16(n－y) ²= 3n(8y－5n)

2 . 4(c+2d)²－25(3c－d)²=(17c－d)(9d－13c)

Prove: L.H.S. = 4(c+2d)²－25(3c－d)²

= [2(c+2d)]^2 - [5(3c-d)]^2

= [2(c+2d)-5(3c-d)] [2(c+2d)+5(3c-d)]

= (2c+4d-15c+5d)(2c+4d+15c-5d)

= (-13c+9d)(17c-d)

= (17c-d)(9d-13c)

= R.H.S.

SO , 4(c+2d)²－25(3c－d)²=(17c－d)(9d－13c)

(n－4y) ²－16(n－y) ²= 3n(8y－5n)
L.H.S. = (n－4y) ²－16(n－y) ²
= (n2-8ny 16y2)-16(n2-2ny y2)
= n2-8ny 16y2-16n2 32ny-16y2
= -15n2 24ny
R.H.S. = 3n(8y－5n)
= 24ny-15n2
∴L.H.S. = R.H.S.

4(c 2d)²－25(3c－d)²=(17c－d)(9d－13c)
L.H.S. = 4(c 2d)²－25(3c－d)²
= 4(c2 4cd 4d2) – 25(9c2-6cd d2)
= 4c2 16cd 16d2 – 225c2 150cd-25d2
= -221 c2 166cd-9d2
R.H.S. =(17c－d)(9d－13c)
= 153cd-221 c2 -9d2 13cd
= -221c2+166cd-9d2
∴L.H.S. = R.H.S.