F.3續因式分解

1.
a)
5b ... -a
b_ ... 3a
_______
(5b)(3a) + (-a)(b) = 14ab

5b² + 14ab - 3a²
= (5b - a)(b + 3a)

b)
令 b = (x - y) 及 a = x
則 5(x² - 2xy + y²) + 14x(x - y) - 3x²
= 5(x - y)² + 14x(x - y) - 3x²
= 5b² + 14ab - 3a²
= (5b - a)(b + 3a)
= [5(x - y) - x] [(x - y) + 3x]
= (4x - 5y)(4x - y)


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2.
a)
3x ... +2y
2x ... -5y
_______
(3x)(-5y) + (2x)(2y) = -11xy

6x² - 11xy - 10y²
= (3x + 2y)(2x - 5y)

b)
3x ... +2y
2x ... +5y
_______
(3x)(5y) + (2x)(2y) = 19xy

6x² + 11xy + 10y²
= (3x + 2y)(2x + 5y)

c)
9(6x² - 11xy - 10y²) - 4(6x² + 19xy + 10y²)
= 9(3x + 2y)(2x - 5y) - 4(3x + 2y)(2x + 5y)
= (3x + 2y) [9(2x - 5y) - 4(2x + 5y)]
= (3x + 2y)(18x - 45y - 8x - 20)
= (3x + 2y)(10x - 65y)
= 5(3x + 2y)(2x - 13y)

1a) 5b-1a
b+3a
--------------
15ab-1ab=14ab

=(5b-1a)(b+3a)

b) 5識....sor><

2a) 3x+2y
2x-5y
----------------
-15xy+4xy=-11xy

=(3x+2y)(2x-5y)

b) 3x+2y
2x+5y
--------------
15xy+4xy=19xy

=(3X+2y)(2x+5y)

c) 5識....sor><

我學完不耐^^有d5識,5好意思><