整式加减的题目及答案

整式加减的题目及答案一、选择题1.已知\(a=3\)，\(b=-2\)，\(c=5\)，下列哪个表达式的结果为0？A.\(a+b-c\)B.\(a-b+c\)C.\(a+b+c\)D.\(a-b-c\)答案：B2.计算\(2x^2-3x+4-(x^2+2x-5)\)的结果。A.\(x^2-5x+9\)B.\(x^2-5x+1\)C.\(x^2-x+9\)D.\(x^2-x+1\)答案：A3.合并同类项\(3x^2-2x+4x-7x^2+5\)的结果是什么？A.\(-4x^2+2x+5\)B.\(-4x^2+6x+5\)C.\(-4x^2+7x+5\)D.\(-4x^2+3x+5\)答案：D4.计算\(4x^2-3x+2-2x^2+5x-4\)的结果。A.\(2x^2+2x-2\)B.\(2x^2+2x+2\)C.\(2x^2+2x-6\)D.\(2x^2-2x+2\)答案：A5.合并同类项\(5x^3-3x^2+2x-7+2x^3-4x+x^2\)的结果是什么？A.\(7x^3-2x^2-2x-7\)B.\(7x^3-2x^2+2x-7\)C.\(7x^3-2x^2-2x+7\)D.\(7x^3-2x^2+2x+7\)答案：B二、填空题6.计算\(3x^2-2x+1+(x^2-4x+3)\)的结果，并填空：\(______\)。答案：\(4x^2-6x+4\)7.合并同类项\(2x^2+3x-5-(x^2-4x+2)\)的结果，并填空：\(______\)。答案：\(x^2+7x-7\)8.计算\(4y^2-3y+5-2y^2+y-3\)的结果，并填空：\(______\)。答案：\(2y^2-2y+2\)9.合并同类项\(7z^3-2z^2+5z-3+3z^3-4z+2z^2\)的结果，并填空：\(______\)。答案：\(10z^3+5z-3\)10.计算\(5m^2-2m-3+3m^2-4m+7\)的结果，并填空：\(______\)。答案：\(8m^2-6m+4\)三、解答题11.已知\(a=2\)，\(b=-1\)，\(c=4\)，求\(a^2+b^2+c^2-(a^2-2ab+b^2)\)的值。答案：\[\begin{align}a^2+b^2+c^2-(a^2-2ab+b^2)&=a^2+b^2+c^2-a^2+2ab-b^2\\&=2ab+c^2\\&=2\cdot2\cdot(-1)+4^2\\&=-4+16\\&=12\end{align}\]12.计算\(3x^2-5x+7-2(x^2+3x-2)\)的结果，并合并同类项。答案：\[\begin{align}3x^2-5x+7-2(x^2+3x-2)&=3x^2-5x+7-2x^2-6x+4\\&=x^2-11x+11\end{align}\]13.合并同类项\(4p^3-3p^2+2p+5-(2p^3-p^2+3p-7)\)。答案：\[\begin{align}4p^3-3p^2+2p+5-(2p^3-p^2+3p-7)&=4p^3-3p^2+2p+5-2p^3+p^2-3p+7\\&=2p^3-2p^2-p+12\end{align}\]14.计算\(5q^2-3q+2-3(q^2+2q-1)\)的结果，并合并同类项。答案：\[\begin{align}5q^2-3q+2-3(q^2+2q-1)&=5q^2-3q+2-3q^2-6q+3\\&=2q^2-9q+5\end{align}\]15.合并同类项\(6r^3-4r^2+3r-2-(3r^3+2r^2-r+1)\)。答案：\[\begin{align}6r^3-4r^2+3r-