xy+3x-2y-6以及x的4平方+3x的平方+4,最後設a+b=8,ab=3 a平方加b平方 a3次方加b的三次方 a-b?

1. xy + 3x - 2y - 6
= x(y + 3) - 2(y + 3)
= (x - 2)(y + 3)

2. x⁴＋3x²＋4
＝x⁴＋4x²＋4－x²
= (x²＋2)²－x²
= (x²＋x＋2)(x²－x＋2)

3. a² + b²
= (a² + 2ab + b²) - 2ab
= (a + b)² - 2ab
= 8² - 2 × 3
= 58

a³ + b³
= (a + b)(a² - ab + b²)
= (a + b)[(a² + b²) - ab]
= 8 × (58 - 3)
= 440

若 a＞b，則 a－b
= √(a－b)²
= √(a²＋b²－2ab)
= √(58－2 × 3]
= √52
= 2√13
若 a＜b，則 a－b＝-2√13

1.
xy + 3x - 2y - 6
= (xy + 3x) - (2y + 6)
= x(y + 3) - 2(y + 3)
= (x - 2)(y + 3) ...... [答案]


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2.
x⁴ + 3x² + 4 不可因式分解

若為 x⁴ + 3x² - 4，則：
x⁴ + 3x² - 4
= (x²)² + 3(x²) - 4
= (x² + 1)(x² - 4)
= (x² + 1)(x² - 2²)
= (x² + 1)(x + 2)(x - 2) ...... [答案]


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3.
a² + b²
= (a² + 2ab + b²) - 2ab
= (a + b)² - 2ab
= 8² - 2 × 3
= 58 ...... [答案]

a³ + b³
= (a + b)(a² - ab + b²)
= (a + b)[(a² + b²) - ab]
= (a + b)[(a² + 2ab + b²) - 3ab]
= (a + b)[(a + b)² - 3ab]
= 8 × [8² - 3 × 3]
= 8 × 55
= 440 ...... [答案]

a - b
= ±√(a - b)²
= ±√[(a + b)² - 4ab]
= ±√[8² - 4 × 3]
= ±√52
= ±2√13 ...... [答案]