math!! 中2 急...

1) a2/64 - 9b2/4
=(a/8)2 – (3b/2)2
=(a/8 – 3b/2)(a/8 + 3b/2) 可再化為(a – 12b)(a + 12b) / 64
2) 289 – x6y4
= 172 – (x3y2)2
= (17 – x3y2)(17 + x3y2)
3) 3x6 – 48x4 + 192x2
= 3x2(x4 – 16x2 + 64)
= 3x2(x2 - 8)2 也可化為 3x2(x - √8)2(x + √8)2
4) rx – ry + ty – tx
= r(x – y) – t(x – y)
= (r – t)(x – y)
5) (x + y)(2x – y) – 3x – 3y
= (x + y)(2x – y) – 3(x + y)
= (x + y)(2x – y – 3)
6) (x + y)(2a – 3b) + (x + y)(2b – c)
= (x + y)(2a – 3b + 2b – c)
= (x + y)(2a – b – c)
7) 27 – x3
= 33 – x3
= (3 – x)(9 + 3x + x2)
8) 16m3 + 2
= 2(8m3 + 1)
= 2[(2m)3 + 13]
= 2(2m + 1)[(2m)2 – (2m) + 1]
= 2(2m + 1)[4m2 – 2m + 1]
展開以下各式
1) (6a – 5b)2 – (a – 2b)2
= (6a – 5b – a + 2b)(6a – 5b + a – 2b)
= (5a – 3b)(7a – 7b)
= 35a2 – 21ab – 35ab + 21b2
= 35a2 – 56ab + 21b2
2) (x + 1)2(x – 1)2
= (x2 – 1)2
= x4 – 2x2 + 1
證明以下各恒等式。
1) 3(y + 1) + 2(y + 6) ≡ 5(y + 3)
3(y + 1) + 2(y + 6)
= 3y + 3 + 2y + 12
= 5y + 15
= 5(y + 3)
2) (a – b)(c – d) + (a – d)(b – c) ≡ (a – c)(b – d)
(a – b)(c – d) + (a – d)(b – c)
= ac – bc – ad + bd + ab – bd – ac + cd
= –bc – ad + ab + cd
= –bc + cd – ad + ab
= –c(b – d) + a(b – d)
= (a – c)(b – d)