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8) 1-a+a^2-a^39) xyz-1-y+xz12) m(1-2n^2)+n(m^2-21)17) (x+y)^2 -4(x-y)^218) 18-8(1-a)^220) (a+1)^4 - 123) (x-1)^2 -2(x-1)+1 25) 2x^2 +7x +326) 8a^2 -ab -7b^2 27) 6x^2 -17xy^2 +10y^429) ... 顯示更多 8) 1-a+a^2-a^3 9) xyz-1-y+xz 12) m(1-2n^2)+n(m^2-21) 17) (x+y)^2 -4(x-y)^2 18) 18-8(1-a)^2 20) (a+1)^4 - 1 23) (x-1)^2 -2(x-1)+1 25) 2x^2 +7x +3 26) 8a^2 -ab -7b^2 27) 6x^2 -17xy^2 +10y^4 29) mn+4-2(m+n) 30) ab^2 -2c^2-bc(1-2a) 31) p^2-q^2-p-q 32) 4a^2-b+2ab-1 33) a^2 b^2-4b^2-a^2+4 34) 4a^2+a-4a^3-1 35) x^2-2x+1-y^2 36) x^2+y^2-z^2+2xy 吾該.識幾多.都幫幫忙.. 趕...!

最佳解答:

8) 1 – a + a^2 – a^3 = 1 – a + a^2(1 – a) = (1 – a)(1 + a^2) 9) xyz – 1 – y + xz = xyz + xz – (1 + y) = xz(1 + y) – (1 + y) = (1 + y)(xz – 1) 12) m(1 – 2n^2) + n(m^2 – 2) (TYPO??) = m – 2mn^2 + m^2n – 2n = m + m^2n – 2n – 2mn^2 = m(1 + mn) – 2n(1 + mn) = (m – 2n)(mn + 1) 17) (x + y)^2 – 4(x – y)^2 = (x + y)^2 – (2x – 2y)^2 = (x + y + 2x – 2y)(x + y – 2x + 2y) = (3x – y)(3y – x) 18) 18 – 8(1 – a)^2 = 2[9 – 4(1 – a)^2] = 2[3^2 – (2 – 2a)^2] = 2(3 + 2 – 2a)(3 – 2 + 2a) = 2(5 – 2a)(1 + 2a) 20) (a+1)^4 – 1 = [(a+1)^2]^2 – 1 = [(a+1)^2 + 1][(a+1)^2 – 1] = (a^2 + 2a + 2)(a + 1 + 1)(a + 1 – 1) = a(a + 2)(a^2 + 2a + 2) 23) (x-1)^2 – 2(x-1) + 1 =[(x-1) – 1]^2 = (x – 2)^2 25) 2x^2 + 7x +3 = 2x^2 + x + 6x + 3 = x(2x + 1) + 3(2x + 1) = (2x + 1)(x + 3) 26) 8a^2 – ab – 7b^2 = 8a^2 – 8ab + 7ab – 7b^2 = 8a(a – b) + 7b(a – b) =(a – b)(8a + 7b) 27) 6x^2 – 17xy^2 +10y^4 = 6x^2 – 12xy^2 – 5xy^2 + 10y^4 = 6x(x – 2y^2) – 5y^2(x – 2y^2) = (6x – 5y^2)(x – 2y^2) 29) mn + 4 – 2(m + n) = mn + 4 – 2m – 2n = mn – 2m – 2n + 4 = m(n – 2) – 2(n – 2) = (n – 2)(m – 2) 30) ab^2 – 2c^2 – bc(1 – 2a) = ab^2 – 2c^2 – bc + 2abc = ab^2 – bc + 2abc – 2c^2 = b(ab – c) + 2c(ab – c) = (b + 2c)(ab – c) 31) p^2 – q^2 – p – q = (p + q)(p – q) – (p + q) = (p + q)(p – q – 1) 32) 4a^2 – b + 2ab – 1 = 4a^2 – 1 + 2ab – b = (2a + 1)(2a – 1) + b(2a – 1) = (2a – 1)(2a + b + 1) 33) a^2b^2 – 4b^2 – a^2 + 4 = b^2(a^2 – 4) – (a^2 – 4) = (b^2 – 1)(a^2 – 4) = (b – 1)(b + 1)(a – 2)(a + 2) 34) 4a^2 + a – 4a^3 – 1 = 4a^2 – 4a^3 – 1 + a = 4a^2(1 – a) – (1 – a) = (1 – a)(4a^2 – 1) = (1 – a)(2a + 1)(2a – 1) 35) x^2 – 2x + 1 – y^2 = (x – 1)^2 – y^2 = (x + y – 1)(x – y – 1) 36) x^2 + y^2 – z^2 + 2xy = x^2 + 2xy + y^2 – z^2 = (x + y)^2 – z^2 = (x + y + z)(z + y – z)

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