15. 先化简,再求值.
(1) $3a^2b + (-a^2b + 3ab^2) - (2a^2b - ab^2)$,其中 $a = 2$,$b=-\frac{1}{2}$;
(2) $3xy^2 - [2x^2y - 3(x^2y - xy^2)]$,其中 $x = 2$,$y=-1$;
(3) 已知 $A = 5x^2 -4xy + y$,$B = x^2 +3xy -2y$. 若 $2A -3B$ 的值与 $y$ 无关,求 $x$ 的值.
(1) $3a^2b + (-a^2b + 3ab^2) - (2a^2b - ab^2)$,其中 $a = 2$,$b=-\frac{1}{2}$;
(2) $3xy^2 - [2x^2y - 3(x^2y - xy^2)]$,其中 $x = 2$,$y=-1$;
(3) 已知 $A = 5x^2 -4xy + y$,$B = x^2 +3xy -2y$. 若 $2A -3B$ 的值与 $y$ 无关,求 $x$ 的值.
答案
15.(1)原式$= 3a^2b-a^2b+3ab^2-2a^2b+ab^2 = 4ab^2,$
当$a = 2,\ b=-\frac{1}{2}$时,
$4ab^2=4× 2× (-\frac{1}{2})^2=8× \frac{1}{4}=2;$
(2)原式$= 3xy^2-( 2x^2y-3x^2y+3xy^2 )$
$= 3xy^2-2x^2y+3x^2y-3xy^2$
$= x^2y,$
当$x = 2,\ y = -1$时,原式$= 2^2× (-1 )= -4.$
(3)$\because A = 5x^2-4xy+y,\ B = x^2+3xy-2y,$
$\therefore 2A-3B$
$= 2( 5x^2-4xy+y ) -3( x^2+3xy-2y )$
$= 10x^2-8xy+2y-3x^2-9xy+6y$
$= 7x^2-17xy+8y$
$= 7x^2-( 17x-8 ) y.$
$\because 2A-3B$的值与$y$无关,
$\therefore 17x-8 = 0,$
解得:$x=\frac{8}{17}.$
当$a = 2,\ b=-\frac{1}{2}$时,
$4ab^2=4× 2× (-\frac{1}{2})^2=8× \frac{1}{4}=2;$
(2)原式$= 3xy^2-( 2x^2y-3x^2y+3xy^2 )$
$= 3xy^2-2x^2y+3x^2y-3xy^2$
$= x^2y,$
当$x = 2,\ y = -1$时,原式$= 2^2× (-1 )= -4.$
(3)$\because A = 5x^2-4xy+y,\ B = x^2+3xy-2y,$
$\therefore 2A-3B$
$= 2( 5x^2-4xy+y ) -3( x^2+3xy-2y )$
$= 10x^2-8xy+2y-3x^2-9xy+6y$
$= 7x^2-17xy+8y$
$= 7x^2-( 17x-8 ) y.$
$\because 2A-3B$的值与$y$无关,
$\therefore 17x-8 = 0,$
解得:$x=\frac{8}{17}.$
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