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Form 3 Maths Factorize
發問:
1 (a) Factorize y3 + 27 (b) Hence, factorize y3 - 7y + 6 2. (a) Factorize 4x2 - 25x + 36 (b) Hence, factorize 4u2 - 25u2 + 36
最佳解答:
1 (a) Factorize y3 + 27 (b) Hence, factorize y3 - 7y + 6 (a) a^3+b^3= (a+b)(a^2?ab+b^2) y3 + 27 = y3 + 33 = (y + 3)(y^2 - 3y + 3^2) (b) y3 - 7y + 6 = y3 + 27 - 27 - 7y + 6 = (y3 + 27) - 7y - 21 = (y + 3)(y^2 - 3y + 3^2) - 7(y + 3) = (y + 3)(y^2 - 3y + 9 - 7) = (y + 3)(y^2 - 3y + 27) 2013-09-29 13:55:57 補充： 4x2 - 25x + 36 =(x - 4)(x - 9)
其他解答:
1 (a) Factorize y^3+27 Sol y^3+27 =y^3+3^3 =(y+3)(y^2－3y+3^2) =(y+3)(y^2－3y+9) (b) Hence, factorize y^3－7y+6 Sol y^3－7y+6 =(y^3+27)+(－7y－21) =(y+3)(y^2－3y+9)－7(y+3) =(y^3－3y+2)(y+3) =(y－1)(y－2)(y+3) 2. (a) Factorize 4x^2－25x+36 Sol 4x^2－25x+36 =(4x－9)(x－4) (b)Hence，factorize 4u^4－25u^2+36 Sol 4u^4－25u^2+36 =(4u^2－9)(u^2－4) =(2u－3)(2u+3)(u－2)(u+2)
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