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1. $ 3-(m-2)= $______
答案
-m+5
解析
$3 - m + 2 = -m + 5$
2. $ 4x+5(x-1)= $______
答案
9x-5
解析
$4x + 5(x - 1)$
$=4x + 5x - 5$
$=9x - 5$
$=4x + 5x - 5$
$=9x - 5$
3. $ 3x-5y+2x-3y= $______
答案
5x-8y
解析
$3x+2x-5y-3y=5x-8y$
4. $ 2a^{2}+3b^{2}-4a^{2}-2b^{2}= $______
答案
-2a²+b²
解析
$2a^{2}+3b^{2}-4a^{2}-2b^{2}$
$=(2a^{2}-4a^{2})+(3b^{2}-2b^{2})$
$=-2a^{2}+b^{2}$
$=(2a^{2}-4a^{2})+(3b^{2}-2b^{2})$
$=-2a^{2}+b^{2}$
5. $ m+n-2(m-n)= $______
答案
-m+3n
解析
$m + n - 2(m - n)$
$= m + n - 2m + 2n$
$= -m + 3n$
$= m + n - 2m + 2n$
$= -m + 3n$
6. $ -3(m-n)-m+n= $______
答案
-4m+4n
解析
$-3(m-n)-m+n=-3m+3n-m+n=-4m+4n$
7. $ 2(2m+n)-(m-3n)= $______
答案
3m+5n
解析
$2(2m+n)-(m-3n)$
$=4m+2n-m+3n$
$=3m+5n$
$=4m+2n-m+3n$
$=3m+5n$
8. $ 2(m+3n)+3(2n-m)= $______
答案
-m+12n
解析
$2(m + 3n) + 3(2n - m)$
$=2m + 6n + 6n - 3m$
$=(2m - 3m) + (6n + 6n)$
$=-m + 12n$
$=2m + 6n + 6n - 3m$
$=(2m - 3m) + (6n + 6n)$
$=-m + 12n$
9. (6x^{2}-7x-5)-( )______)= 5x^{2}-2x+3
答案
x²-5x-8
解析
设括号内的式子为$A$，则原式可写为$(6x^{2}-7x-5)-A = 5x^{2}-2x+3$，解得$A=(6x^{2}-7x-5)-(5x^{2}-2x+3)=6x^{2}-7x-5 -5x^{2}+2x-3=x^{2}-5x-8$。$x^{2}-5x-8$
10. $ x-y 与 -\frac{2}{5}x+3y $的差是______.
答案
$\frac{7}{5}x-4y$
解析
$(x - y) - \left(-\frac{2}{5}x + 3y\right)$
$= x - y + \frac{2}{5}x - 3y$
$= \left(1 + \frac{2}{5}\right)x + (-1 - 3)y$
$= \frac{7}{5}x - 4y$
$= x - y + \frac{2}{5}x - 3y$
$= \left(1 + \frac{2}{5}\right)x + (-1 - 3)y$
$= \frac{7}{5}x - 4y$
二、解答题
11. $ \frac{3}{2}(4x^{2}y-5xy^{2})-(3yx^{2}-4xy^{2}) $ 12. $ 5x^{2}-[x^{2}-2x-2(x^{2}-3x+1)] $
13. $ 2(4x^{2}y+xy)-3x^{2}y-7x-5yx-4(y^{2}x+2x^{2}y+1) $
14. 已知$ A= x^{3}-2y^{3}+3x^{2}y+xy^{2}-3xy+4,B= y^{3}-x^{3}-4x^{2}y-3xy-3xy^{2}+3 $,$ C= y^{3}+x^{2}y+2xy^{2}+6xy-6 $,试化简：$ A+B+C $.
11. $ \frac{3}{2}(4x^{2}y-5xy^{2})-(3yx^{2}-4xy^{2}) $ 12. $ 5x^{2}-[x^{2}-2x-2(x^{2}-3x+1)] $
13. $ 2(4x^{2}y+xy)-3x^{2}y-7x-5yx-4(y^{2}x+2x^{2}y+1) $
14. 已知$ A= x^{3}-2y^{3}+3x^{2}y+xy^{2}-3xy+4,B= y^{3}-x^{3}-4x^{2}y-3xy-3xy^{2}+3 $,$ C= y^{3}+x^{2}y+2xy^{2}+6xy-6 $,试化简：$ A+B+C $.
答案
11. 3x²y-$\frac{7}{2}$xy² 12. 6x²-4x+2 13. -7x²y²-3xy-7x-4 14. A+B+C=4+3-6=1
解析
11. $\frac{3}{2}(4x^{2}y - 5xy^{2}) - (3yx^{2} - 4xy^{2})$
$=6x^{2}y - \frac{15}{2}xy^{2} - 3x^{2}y + 4xy^{2}$
$=(6x^{2}y - 3x^{2}y) + (-\frac{15}{2}xy^{2} + 4xy^{2})$
$=3x^{2}y - \frac{7}{2}xy^{2}$
12. $5x^{2} - [x^{2} - 2x - 2(x^{2} - 3x + 1)]$
$=5x^{2} - [x^{2} - 2x - 2x^{2} + 6x - 2]$
$=5x^{2} - [-x^{2} + 4x - 2]$
$=5x^{2} + x^{2} - 4x + 2$
$=6x^{2} - 4x + 2$
13. $2(4x^{2}y + xy) - 3x^{2}y - 7x - 5yx - 4(y^{2}x + 2x^{2}y + 1)$
$=8x^{2}y + 2xy - 3x^{2}y - 7x - 5xy - 4xy^{2} - 8x^{2}y - 4$
$=(8x^{2}y - 3x^{2}y - 8x^{2}y) + (2xy - 5xy) - 4xy^{2} - 7x - 4$
$=-3x^{2}y - 3xy - 4xy^{2} - 7x - 4$
14. $A + B + C$
$=(x^{3} - 2y^{3} + 3x^{2}y + xy^{2} - 3xy + 4) + (y^{3} - x^{3} - 4x^{2}y - 3xy - 3xy^{2} + 3) + (y^{3} + x^{2}y + 2xy^{2} + 6xy - 6)$
$=x^{3} - 2y^{3} + 3x^{2}y + xy^{2} - 3xy + 4 + y^{3} - x^{3} - 4x^{2}y - 3xy - 3xy^{2} + 3 + y^{3} + x^{2}y + 2xy^{2} + 6xy - 6$
$=(x^{3} - x^{3}) + (-2y^{3} + y^{3} + y^{3}) + (3x^{2}y - 4x^{2}y + x^{2}y) + (xy^{2} - 3xy^{2} + 2xy^{2}) + (-3xy - 3xy + 6xy) + (4 + 3 - 6)$
$=1$
$=6x^{2}y - \frac{15}{2}xy^{2} - 3x^{2}y + 4xy^{2}$
$=(6x^{2}y - 3x^{2}y) + (-\frac{15}{2}xy^{2} + 4xy^{2})$
$=3x^{2}y - \frac{7}{2}xy^{2}$
12. $5x^{2} - [x^{2} - 2x - 2(x^{2} - 3x + 1)]$
$=5x^{2} - [x^{2} - 2x - 2x^{2} + 6x - 2]$
$=5x^{2} - [-x^{2} + 4x - 2]$
$=5x^{2} + x^{2} - 4x + 2$
$=6x^{2} - 4x + 2$
13. $2(4x^{2}y + xy) - 3x^{2}y - 7x - 5yx - 4(y^{2}x + 2x^{2}y + 1)$
$=8x^{2}y + 2xy - 3x^{2}y - 7x - 5xy - 4xy^{2} - 8x^{2}y - 4$
$=(8x^{2}y - 3x^{2}y - 8x^{2}y) + (2xy - 5xy) - 4xy^{2} - 7x - 4$
$=-3x^{2}y - 3xy - 4xy^{2} - 7x - 4$
14. $A + B + C$
$=(x^{3} - 2y^{3} + 3x^{2}y + xy^{2} - 3xy + 4) + (y^{3} - x^{3} - 4x^{2}y - 3xy - 3xy^{2} + 3) + (y^{3} + x^{2}y + 2xy^{2} + 6xy - 6)$
$=x^{3} - 2y^{3} + 3x^{2}y + xy^{2} - 3xy + 4 + y^{3} - x^{3} - 4x^{2}y - 3xy - 3xy^{2} + 3 + y^{3} + x^{2}y + 2xy^{2} + 6xy - 6$
$=(x^{3} - x^{3}) + (-2y^{3} + y^{3} + y^{3}) + (3x^{2}y - 4x^{2}y + x^{2}y) + (xy^{2} - 3xy^{2} + 2xy^{2}) + (-3xy - 3xy + 6xy) + (4 + 3 - 6)$
$=1$
