(4x+5y)*-(2x-y)*因式分解 *是平方

问题描述:

(4x+5y)*-(2x-y)*因式分解 *是平方

应该是(4x+5y)²-(2x-y)²吧
(4x+5y)²-(2x-y)²=(4x+5y+2x-y)(4x+5y-2x+y)=(6x+4y)(2x+6y)=4(3x+2y)(x+3y)

(4x+5y)^2-(2x-y)^2
=(4x+5y+2x-y)(4x+5y-(2x-y))
=(6x+4y)(2x+6y)
=4(3x+2y)(x+3y)

首先看到平方和减号就想到用平方差公式
(4x+5y)^2-(2x-y)^2
=(4x+5y+2x-y)(4x+5y-(2x-y))
=(6x+4y)(2x+6y)
=4(3x+2y)(x+3y)

[4x+5y+(2x-y)][4x+5y-(2x-y)]=(6x+4y)(2x+6y)=4(3x+2y)(x+3y)

(6x+4y)(2x+6y)=4(3x+2y)(x+3y)