因式分解4X^2-9y^2-4x+1

Question

1. 4X^2-9y^2-4x+1


2. 4x^2 - y^2 - 2y - 1

百思不解......

Answer 1

1. 4X^2-9y^2-4x+1
= 4X^2 - 4X + 1 - 9Y^2
= (2X - 1)^2 - (3Y)^2
= (2X + 3Y - 1)(2X - 3Y - 1) <----a^2 - b^2 = (a+b)(a-b)


2. 4x^2 - y^2 - 2y - 1
= 4x^2 - (y^2 + 2y + 1)
= (2x)^2 - (y + 1)^2
= (2x + y + 1)[2x - (y + 1)]
= (2x + y + 1)(2x - y - 1) <----a^2 - b^2 = (a+b)(a-b)

解題技巧:
由於多項式中, 並沒有xy這項, 所以可以試著先分類, 然後先分別求取x和y的因式, 求完後再做一次x和y的因式

Answer 2

4X^2-9y^2-4x+1
=(4X^2-4x+1)-9y^2
=(2x-1)^2-(3y)^2
=(2x-1-3y)(2x+3y)

4x^2 - y^2 - 2y - 1
=4x^2 - (y^2 + 2y + 1)
=(2x)^2 - (y+1)^2
=(2x-y-1)(2x+y+1)

都是用到平方差的公式

Answer 3

1. 4x²-4x+1-9y²=(2x-1)²-(3y)²=(2x+3y-1)(2x-3y-1)

2. 4x²-(y²+2y+1)=(2x)²-(y+1)²=(2x+y+1)(2x-y-1)