(2x-y)(y+2x)-(2y+x)(2y-x),其中x=1化简求值

更新时间2022-06-24 14:19:15

(2x-y)(y+2x)-(2y+x)(2y-x)

=[(2x²-y²]-[(2y)²-x²]

=4x²-y²-4y²+x²

=5x²-5y²

//

(2x-y+3z)(-2x-y-3z)-(x+2y-3z)²

=[-y+(2x+3z)][-y-(2x+3z)]-[2y+(x-3z)]²

=(-y)²-(2x+3z)²-(2y)²-2(2y)(x-3z)-(x-3z)²

=y²-4y²-(4xy-12yz)-(4x²+12xz+9z²)-(x²-6xz+9z²)

=-3y²-5x²-18z²-4xy+12yz-6xz

=-3*1-5*1-18*1-4(-1)+12(-1)-6*1

=-3-5-18+4-12-6

=-40

直接代入

原式=(2+1+3)(-2+1-3)-(1-2-3)²

=6*(-4)-(-4)²

=-24-16

=-40

多简单

(2x-y)(y+2x)-(2y+x)(2y-x)

=（4x²-y²)+(x²-4y²)

=4x²-y²+x²-4y²

=5(x²-y²)

=5×(1-y²)

=5-5y²

(2x-y+3z)(-2x-y-3z)-(x+2y-3z)²

=-(2x-y+3z)(2x+y+3z)-(x+2y-3z)²

=-(2x+3z)²+y²-(x+2y-3z)²

=-(2×1+3×1)²+(-1)²-(1-2×1+3×1)²

=-25+1-4

=-28