整式加减与化简求值专项训练
一、选择题
1. 下列合并同类项正确的是( )
A. $3a + 2a = 5$ B. $3a + 2b = 5ab$
C. $5a^{2} – a^{2} = 4$ D. $7a^{2} – 2a^{2} = 5a^{2}$
2. 下列整式中，不是同类项的是( )
A. $100x$和$10x$ B. $3ab$和$ab$
C. $m^{2}n$和$nm^{2}$ D. $2a^{2}b$和$3ab^{2}$
3. 已知$a = 3$，$b = – 2$，则$3a^{2} – 2ab + 4b^{2}$的值为( )
A. $23$ B. $17$ C. $27$ D. $- 17$
二、填空题
1. 合并同类项：$5x – 7x =$____．
2. 已知$x = 2$，$y = – 3$，则$3x^{2} – 2y^{2} =$____．
3. 若$a^{2} + 2ab + b^{2} = 10$，则$a + b =$____．
三、解答题
1. 合并同类项：
(1) $3x – 2x + 5x$
(2) $7a^{2} – 2a^{2} – 5a^{2} + 4$
2. 化简求值：
(1) $3x^{2} – [2x – (x – 3)]$，其中$x = 2$
(2) $4(a^{2}b – ab) – [3a^{2}b – (3ab – 1)]$，其中$a = – 1$，$b = 2$
3. 已知$a + b = 7$，$ab = 6$，求$3(a + b) – 2ab$的值．
四、综合题
1. 已知$x + y = 8$，$xy = 6$，求$2(x + y) – 3xy$的值．
2. 已知$a – b = 4$，$ab = – 3$，求$2(a – b) – 3ab$的值．
【答案】
一、选择题
1. D
2. D
3. A
二、填空题
1. $- 2x$
2. $17$
3. $5$
三、解答题
1. (1) 解：$3x – 2x + 5x = 6x$
(2) 解：$7a^{2} – 2a^{2} – 5a^{2} + 4 = – 2a^{2} + 4 = 4$
2. (1) 解：$3x^{2} – [2x – (x – 3)] = 3x^{2} – 2x + x – 3 = 3x^{2} – x – 3$
当$x = 2$时，原式$= 3 \times 2^{2} – 2 \times 2 – 3 = 12 – 4 – 3 = 5$
(2) 解：$4(a^{2}b – ab) – [3a^{2}b – (3ab – 1)] = 4a^{2}b – 4ab – 3a^{2}b + 3ab – 1 = a^{2}b – ab – 1$
当$a = – 1$，$b = 2$时，原式$= (- 1)^{2} \times 2 – (- 1) \times 2 – 1 = 2 + 2 – 1 = 3$
3. 解：$3(a + b) – 2ab = 3 \times 7 – 2 \times 6 = 21 – 12 = 9$
四、综合题
1. 解：$2(x + y) – 3xy = 2 \times 8 – 3 \times 6 = 16 – 18 = – 2$
2. 解：$2(a – b) – 3ab = 2 \times 4 – 3 \times ( – 3) = 8 + 9 = 17$