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因式分解 & 解不等式 (20點)

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發問:

1. 4wx + wy – 8xz^2 + 2yz^22. p^3 – ps – st^2 + p^2t^23. ( x + y )^2 – 2( x + y) + 14. x^2 + 2xy + y^2 – 15. 5a^3 ( x – y ) + 25a ^4 (y – x )6. 18( a + b ) ^2 – 32( a + b )7. ab + 24 + 12c – 6b – 2ac – 4a 8. 20p^2 + 60pq + 45q^29. 2x – 4 over 7 不小於 – 210. 1 – 5x over – 3 小於 3

最佳解答:

1. 4wx + wy – 8xz^2 + 2yz^2 = w(4x+y) - 2z^2(4x-y)2. p^3 – ps – st^2 + p^2t^2 = p(p^2 - s) - t^2 (s - p^2) = p(p^2-s) + t^2(p^2 - s) = (p^2-s)(p+t^2)3. ( x + y )^2 – 2( x + y) + 1 Let n = x+y (x+y)^2 - 2(x+y) + 1 = n^2 - 2n + 1 = (n-1)^2 = (x+y-1)^24. x^2 + 2xy + y^2 – 1 = (x+y)^2 - 1 = (x+y+1)(x+y-1)5. 5a^3 ( x – y ) + 25a ^4 (y – x ) = 5a^3 (x-y) - 25a^4(x-y) = 5a^3(x-y)(1-5a)6. 18( a + b ) ^2 – 32( a + b ) = 2(a+b)[9(a+b) - 16] = 2(a+b)(9a+9b-16)7. ab + 24 + 12c – 6b – 2ac – 4a= ab - 4a + 12c – 2ac – 6b + 24= a(b-4) + 2c(6 – a) – 6(b-4)= a(b-4) – 6(b-4) – 2c(a-6)= (b-4)(a-6) – 2c(a-6)= (a-6)(b-4-2c)8. 20p^2 + 60pq + 45q^2= 5(4p^2 + 12pq + 9q^2)= 5[(2p)^2 + 2(2p)(3q) + (3q)^2]= 5(2p+3q)^29. (2x – 4) / 7 ≥ – 22x – 4 ≥ -142x ≥ -10x ≥ -510. (1 – 5x) / – 3 < 31-5x > -910 > 5x5x < 10x < 2

其他解答:

1. 4wx + wy – 8xz^2 + 2yz^2 =w(4x+y)-2z^2(4x+y) =(4x+y)(w-2z^2) 2. p^3 – ps – st^2 + p^2t^2 =p(p^2-s)+t^2(p^2-s) =(p^2-s)(p+t^2) 3. ( x + y )^2 – 2( x + y) + 1 =(x+y)^2-2(x+y)(1)+1^2 =(x+y-1)^2 4. x^2 + 2xy + y^2 – 1 =(x+y)^2-1^2 =(x+y+1)(x+y-1) 5. 5a^3 ( x – y ) + 25a ^4 (y – x ) =5a^3(x-y)-25a^4(x-y) =(5a^3-25a^4)(x-y) =5a^3(1-5a)(x-y) 6. 18( a + b ) ^2 – 32( a + b ) =(a+b)[18(a+b)-32] 7. ab + 24 + 12c – 6b – 2ac – 4a =12c-2ac-6b+ab+24-4a =2c(6-a)-b(6-a)+4(6-a) =(6-a)(2c-b+4) 8. 20p^2 + 60pq + 45q^2 =5(4p^2+12pq+9q^2) =5(2p+3q)^2 9.我唔知你系咪 =2x – 4 over 7 不小於 – 2 =(2x-4)除6 不小於 -2 10.一樣 =1 – 5x over – 3 小於 3 =(1-5x)除-3 小於 3
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