標題:
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Maths
發問:
1)Factorize 54a^4 +16a 2a) Factorize (p2 +q2 )2 -4p2 q2 2b)36x2 -12x -169y2 +26y 3)t2 +(t+3)2 -17
最佳解答:
1) 54a^4 + 16a = 2a(27a^3 + 8) = 2a[(3a)^3 + 2^3] = 2a(3a+2)(9a^2 - 6a + 4) 2)a) (p^2 + q^2)^2 - 4p^2 q^2 = (p^2 + q^2)^2 - (2pq)^2 = (p^2 + q^2 + 2pq)(p^2 + q^2 - 2pq) = (p^2 + 2pq + q^2)(p^2 - 2pq + q^2) = (p+q)^2 (p-q)^2 b) 36x^2 - 12x - 169y^2 + 26y = 36x^2 - 169y^2 - 12x + 26y = (6x)^2 - (13y)^2 - 2(6x - 13y) = (6x+13y)(6x-13y) - 2(6x-13y) = (6x-13y)(6x+13y-2) 3) t^2 + (t+3)^2 - 17 = t^2 + t^2 + 6t + 9 - 17 = 2t^2 + 6t - 8 = 2(t^2 + 3t - 4) = 2(t-1)(t+4)
其他解答:
1) 54a^4 + 16a = 2a(27a^3 + 8) = 2a[(3a)^3 + 2^3] = 2a(3a + 2)(9a^2 - 6a + 4) 2a) (p2q2)2 - 4p2q2 = (p2q2)[(pq)^2 - 2^2] = (p2q2)(pq - 2)(pq + 2) b) 36x^2 - 12x - 169y^2 + 26y = (6x)^2 - (13y)^2 - 2(6x - 13y) = (6x - 13y)(6x + 13y) - 2(6x - 13y) = (6x - 13y)(6x + 13y - 2) 3) t^2 + (t + 3)^2 - 17 = t^2 + t^2 + 6t + 9 - 17 = 2t^2 + 6t - 8 = 2(t^2 + 3t - 4) = 2(t + 4)(t - 1)
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