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標題:

中二簡單factorization~~~

發問:

1.8q^2+2r+4q-2r^2 2.-2q^4+2q^3+q^2-1 3.b^2+4bc+4c^2 4.36x^2+49y^2+84xy 5.h^2-16hk+64k^2 列埋steps唔該哂~

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最佳解答:

1.8q^2 + 2r + 4q - 2r^2 = 2[4q^2 + 2q + 1/4 - 1/4 + r - r^2] = 2[(2q + 1/2)^2 - (r - 1/2)^2] = 2(2q + 1/2 + r - 1/2)(2q + 1/2 - r + 1/2) = 2(2q + r)(2q - r + 1) 2. -2q^4 + 2q^3 + q^2 - 1 = -2q^3(q - 1) + (q - 1)(q + 1) = (q - 1)(-2q^3 + q + 1) = (q - 1)(-2q^3 + 2q^2 - 2q^2 + 2q - q + 1) = (q - 1)[-2q^2(q - 1) - 2q(q - 1) - (q - 1)] = -(q - 1)^2(2q^2 + 2q - 1) 3.b^2 + 4bc + 4c^2 = b^2 + 2bc + 2bc + 4c^2 = b(b + 2c) + 2c(b + 2c) = (b + 2c)^2 4.36x^2 + 49y^2 + 84xy = 36x^2 + 42xy + 42xy + 49y^2 = 6x(6x + 7y) + 7y(6x + 7y) = (6x + 7y)^2 5. h^2 - 16hk + 64k^2 = h^2 - 8hk -8hk + 64k^2 = h(h - 8k) - 8k(h - 8k) = (h - 8k)^2

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