因式分解:(3x-y)(y+3x)-(4x-3y)(3y+4x)

问题描述:

因式分解:(3x-y)(y+3x)-(4x-3y)(3y+4x)

=3xy+9x^2-y^2-3xy-12xy-16x^2+9y^2+12xy
=8y^2-7x^2

(3x-y)(y+3x)-(4x-3y)(3y+4x)=(3x-y)(3x+y)-(4x-3y)(4x+3y)=(3x)²-y²-[(4x)²-(3y)²]= 9x²-y²-16x²+9y²=8y²-7x²