Question

Tseng

請問第十題題如何因式分解

-23
Fe 原
hint
[(ab)
10 x(x²-1)-y(y²-1)+xy(x-y)
2
11. x+64 (X) + 8 + 16x2
=1
(C)
解二次方程式
2
(x²+8)² - (4x)²
(x²+4x+8)(x²-4x+8

Answer 1

qn

x³ - x - y³ + y + xy(x-y)
= x³ - y³ + xy(x - y) - (x - y)
= x³ - y³ - 3xy(x - y) + 4xy(x - y) - (x - y)
= (x - y)³ + (4xy - 1)(x - y)
= (x - y)[ (x - y)² + (4xy - 1) ]
= (x - y)[x² + y² + 2xy - 1]
= (x - y)[ (x+y)² - 1² ]
= (x-y)(x+y-1)(x+y+1)