展開,因式分解快快快快快快快

(ab + 5)(5 - ad)
= ab(5 - ad) + 5(5 - ad)
= 5ab - a²bd + 25 - 5ad
= -a²bd + 5ab - 5ad + 25


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[x - (y/2)]²
= x² - 2x(y/2) + (y/2)²
= x² - xy + (y²/4)


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若 (5x + 2)(x - 3) ≡ Ax² + Bx + C,其中A,B和C都是常數,求A,B和C的值

(5x + 2)(x - 3) ≡ Ax² + Bx + C
5x(x - 3) + 2(x - 3) ≡ Ax² + Bx + C
5x² - 15x + 2x - 6 ≡ Ax² + Bx + C
5x² - 13x - 6 ≡ Ax² + Bx + C

比較兩邊的係數，可得：
A = 5, B = -13, C = -6


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72x² - 2
= 2(36x² - 1)
= 2[(6x)² - (1)²]
= 2(6x + 1)(6x - 1)


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8r - 10s + 12r² - 15rs
= (8r - 10s) + (12r² - 15rs)
= 2(4r - 5s) + 3r(4r - 5s)
= (2 + 3r)(4r - 5s)


=====
4m² + 9n² - 12mn
= 4m² - 12mn + 9n²
= (2m)² - 2(2m)(3n) + (3n)²
= (2m - 3n)²


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1-16x^4
= 1 - (4x²)²
= (1 + 4x²)(1 - 4x²)
= (1 + 4x²)[1 - (2x)²]
= (1 + 4x²)(1 + 2x)(1 - 2x)


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x² + 10x + 25 - 4y²
= (x² + 10x + 25) - 4y²
= [(x)² + 2(x)(5) + (5)²] - 4y²
= (x + 5)² - (2y)²
= [(x + 5) + 2y] [(x + 5) - 2y]
= (x + 2y + 5)(x - 2y + 5)


=====
4a² - 28ab + 49b²
= (2a)² - 2(2a)(7b) + (7b)²
= (2a - 7b)²


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設 a = x - 1 及 b = y + 5

4(x - 1)² - 28(x - 1)(y + 5) + 49(y + 5)² = 4a² - 28ab + 49b²
= (2a)² - 2(2a)(7b) + (7b)²
= (2a - 7b)²
= [2(x - 1) - 7(y + 5)]²
= (2x - 2 - 7y - 35]²
= (2x - 7y - 37)²

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