(1) (C^2+ab)^2 - (a+b)^2乘以C^2

题目

(1) (C^2+ab)^2 - (a+b)^2乘以C^2
(2) 二分之a - 32a^4
(3) 3X^2+ 4XY - Y^2
(4) X^2- 二倍根号二 - 3
(5) 如果2X^3 - 7X^2 -19X +60 有因式2X -5
试讲原式因式分解

答案

(1)(C^2+ab)^2 - (a+b)^2C^2
=[c^2+ab+(a+b)c][c^2+ab-(a+b)c]
=(c^2+ab+ac+bc)(c^2+ab-ac-bc)
(2)a/2-32a^4
=(a/2)(1-64a^3)
=(a/2)(1-4a)(1+4a+16a^2)
(3)3X^2+ 4XY - Y^2
=3[x+(√7+2)/3][x-(√7-2)/3]
(4)X^2-2√2 - 3
=x^2-(√2+1)^2
=(x+√2+1)(x-√2-1)
(5)2X^3 - 7X^2 -19X +60
=2x^3-5x^2-2x^2+5x-24x+60
=x^2(2x-5)-x(2x-5)-12(2x-5)
=(2x-5)(x^2-x-12)
=(2x-5)(x-4)(x+3)