题目内容
已知:A=2x2-3x2y-2xy2,B=x2-2xy2+y3,C=-x2+3x2y-y3.
(1)通过计算:①A+B-C;②A-B+C.
试判断①与②中,哪一个的运算结果的取值与x无关;
(2)在(1)中的运算结果中,任选一个,当x=-1,y=-
时,求它的代数式的值.
(1)通过计算:①A+B-C;②A-B+C.
试判断①与②中,哪一个的运算结果的取值与x无关;
(2)在(1)中的运算结果中,任选一个,当x=-1,y=-
1 |
2 |
(1)∵①A+B-C=(2x2-3x2y-2xy2)+(x2-2xy2+y3)-(-x2+3x2y-y3)
=2x2-3x2y-2xy2+x2-2xy2+y3+x2-3x2y+y3
=(2+1+1)x2+(-3-3)x2y+(-2-2)xy2+(1+1)y3
=4x2-6x2y-4xy2+2y3,
②A-B+C=(2x2-3x2y-2xy2)-(x2-2xy2+y3)+(-x2+3x2y-y3)
=2x2-3x2y-2xy2-x2+2xy2-y3-x2+3x2y-y3
=(2-1-1)x2+(-3+3)x2y+(-2+2)xy2+(-1-1)y3
=-2y3,
所以,②A-B+C的运算结果的取值与x无关;
(2)选①,当x=-1,y=-
时,
原式=4x2-6x2y-4xy2+2y3
=4×(-1)2-6×(-1)2×(-
)-4×(-1)×(-
)2+2×(-
)3
=4+3+1-
=7
;
选②,当x=-1,y=-
时,-2y3=-2×(-
)3=
.
=2x2-3x2y-2xy2+x2-2xy2+y3+x2-3x2y+y3
=(2+1+1)x2+(-3-3)x2y+(-2-2)xy2+(1+1)y3
=4x2-6x2y-4xy2+2y3,
②A-B+C=(2x2-3x2y-2xy2)-(x2-2xy2+y3)+(-x2+3x2y-y3)
=2x2-3x2y-2xy2-x2+2xy2-y3-x2+3x2y-y3
=(2-1-1)x2+(-3+3)x2y+(-2+2)xy2+(-1-1)y3
=-2y3,
所以,②A-B+C的运算结果的取值与x无关;
(2)选①,当x=-1,y=-
1 |
2 |
原式=4x2-6x2y-4xy2+2y3
=4×(-1)2-6×(-1)2×(-
1 |
2 |
1 |
2 |
1 |
2 |
=4+3+1-
1 |
4 |
=7
3 |
4 |
选②,当x=-1,y=-
1 |
2 |
1 |
2 |
1 |
4 |
练习册系列答案
相关题目