整式加減答辯題目及答案

整式加減答辯題目及答案一、單項選擇題1.已知\(a^2+2ab+b^2=(a+b)^2\)，下列哪個選項是正確的？A.\(a^2-2ab+b^2=(a-b)^2\)B.\(a^2+2ab+b^2=(a+b)^2\)C.\(a^2-2ab+b^2=(a+b)^2\)D.\(a^2+2ab+b^2=(a-b)^2\)答案：A2.合并同類項\(3x^2+5x-2x^2+7\)的結(jié)果是：A.\(x^2+5x+7\)B.\(x^2+5x-7\)C.\(x^2-5x+7\)D.\(x^2-5x-7\)答案：A3.將多項式\(x^3-2x^2+3x-4\)與\(-x^3+3x^2-5x+6\)相加，結(jié)果為：A.\(-2x^3+x^2-2x+2\)B.\(-2x^3+x^2-2x-2\)C.\(-2x^3+x^2+2x-2\)D.\(-2x^3+x^2+2x+2\)答案：B4.已知\(x=2\)時，\(3x^2-2x+1=9\)，求\(x=-2\)時該表達(dá)式的值：A.\(-9\)B.\(9\)C.\(-27\)D.\(27\)答案：C5.將\(x^2-4x+4\)因式分解，正確的表達(dá)式是：A.\((x-2)^2\)B.\((x+2)^2\)C.\((x-4)^2\)D.\((x+4)^2\)答案：A二、填空題6.將\(2x^2+3x-5\)與\(-x^2+4x+7\)相加，結(jié)果為\(\boxed{1x^2+7x+2}\)。7.已知\(x+y=5\)和\(x-y=3\)，求\(x^2-y^2\)的值，結(jié)果為\(\boxed{16}\)。8.將\(3x^3-2x^2+x-4\)與\(-2x^3+x^2-3x+5\)相減，結(jié)果為\(\boxed{5x^3-3x^2+4x-1}\)。9.將\(x^2-6x+9\)因式分解，結(jié)果為\(\boxed{(x-3)^2}\)。10.已知\(a=3\)和\(b=4\)，求\(a^2-2ab+b^2\)的值，結(jié)果為\(\boxed{5}\)。三、解答題11.計算表達(dá)式\(4x^2-3x+1\)與\(-2x^2+5x-3\)的和，并簡化結(jié)果。解答：\[\begin{align}(4x^2-3x+1)+(-2x^2+5x-3)&=4x^2-3x+1-2x^2+5x-3\\&=(4x^2-2x^2)+(-3x+5x)+(1-3)\\&=2x^2+2x-2\end{align}\]結(jié)果為\(2x^2+2x-2\)。12.已知\(x=1\)，計算表達(dá)式\(x^2-5x+6\)的值。解答：\[\begin{align}x^2-5x+6&=1^2-5\cdot1+6\\&=1-5+6\\&=2\end{align}\]結(jié)果為\(2\)。13.將多項式\(2x^3-3x^2+4x-5\)與\(-x^3+2x^2-x+3\)相減，并因式分解結(jié)果。解答：\[\begin{align}(2x^3-3x^2+4x-5)-(-x^3+2x^2-x+3)&=2x^3-3x^2+4x-5+x^3-2x^2+x-3\\&=(2x^3+x^3)+(-3x^2-2x^2)+(4x+x)+(-5-3)\\&=3x^3-5x^2+5x-8\end{align}\]因式分解結(jié)果為\((x-1)(3x^2-2x+8)\)。14.計算表達(dá)式\(x^2-4x+4\)的值，當(dāng)\(x=0\)。解答：\[\begin{align}x^2-4x+4&=0^2-4\cdot0+4\\&=4\end{align}\]結(jié)果為\(4\)。15.已知\(a=2\)和\(b=-3\)，計算表達(dá)式\(a^2-b^2\)的值。解答：