Math topic中文

Brackets common factors

use brackets and extract common factors

Practice questions

  1. 1如果代数式x−2y+2x-2y+2的值是55，则2x−4y2x-4y的值是()                    (\quad)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: A. 3          3\:\:\:\:\:\:\:\:\:\: …
  2. 2The equation of a curve is y=x2e2xy = x^2 e^{2x}. Obtain an expression for dydx\dfrac{dy}{dx}. Find the range of values of xx…
  3. 3计算： (1)(94)12−(−9.6)0−(278)−23+(32)−2(1)(\dfrac{9}{4})^{\frac{1}{2}}-(-9.6)^{0}-(\dfrac{27}{8})^{-\frac{2}{3}}+(\dfrac{3}{2})^{-2}； (2)lg⁡5+lg⁡2⋅lg⁡5+(lg⁡2)2+eln⁡3(e(2)\lg 5+\lg 2\boldsymbol{⋅}\lg 5+(\lg 2)^{2}+e^{\ln 3}(e…
  4. 4解方程：14％x−9％(x+10)=7％x+0.214％x-9％(x+10)=7％x+0.2
  5. 5已知x−2y+5=0x-2y+5=0，则4y−2x4y-2x的值为()(\quad) A. 55 B. −5-5 C. 1010 D. −10-10
  6. 6张老板经营两种茶叶：第一种为“采花芽尖”，卖出aa千克总售价为bb元；第二种茶叶为“云顶雾绿”，比第一种茶叶多卖cc千克时，总售价比第一种多cc元。请你帮张老板计算一下，哪一种茶叶单价稍贵些？ ((其中b>a)b>a)…
  7. 7因式分解：a2−9a=a^{2}-9a= ___ ．
  8. 8先化简，再求值：(2x−y)(x−y)−(2x−y)2(2x-y)(x-y)-{{(2x-y)}^{2}}，其中x=−1,y=−2.x=-1,y=-2.
  9. 9(1)先化简，再求值：(a−b)2+b(a−b)(a-b)^{2}+b(a-b)，其中a=2a=2，b=−12b=- \dfrac {1}{2}． (2)先化简，再求值：(3x+2)(3x−2)−5x(x−1)−(2x−1)2(3x+2)(3x-2)-5x(x-1)-(2x-1)^{2}，其中x=−13x=- \dfrac {1}{3}…
  10. 10把多项式ax2−4ay2a{{x}^{2}}-4a{{y}^{2}}分解因式的结果是___.
  11. 11Factorise completely. abc−3c−6+2ababc - 3c - 6 + 2ab Answer ... 80x4−580x^{4} - 5 Answer ...
  12. 12若关于xx、yy的多项式x2−2kxy+y2+6xy−6x^{2}-2kxy+y^{2}+6xy-6中不含xyxy项，则k=k=___.
  13. 13解方程：5(x-2)=4-(2-x)
  14. 14下列各式中，正确的是（ ） A. 4a-（b+c）=4a-b+c B. 4a-（b+c）=4a+b-c C. 4a-（b+c）=4a+b+c D. 4a-（b+c）=4a-b-c
  15. 15、下列去括号正确的是()(\quad) A. −(a+b−c)=−a+b−c  -(a+b-c)=-a+b-c\:\: B. −2(a+b−3c)=−2a−2b+6c -2(a+b-3c)=-2a-2b+6c\: C. −(−a−b−c)=−a+b+c-(-a-b-c)=-a+b+c D. −(a−b−c)=−a+b−c-(a-b-c)=-a+b-c…
  16. 16有一列按一定顺序和规律排列的数： 第11个数是11×2\dfrac{1}{1×2}；第22个数是12×3\dfrac{1}{2×3}；第33个数是13×4… \dfrac{1}{3×4} …对任何正整数nn，第…
  17. 17不等式组{x−2(x−3)>012x+1⩾−3 \begin{cases} \overset{ \dfrac {1}{2}x+1\geqslant -3}{x-2(x-3) > 0}\end{cases}的解集是 ___ ．
  18. 18Factorise the following completely. 45b−18ab−2a2+5a45b - 18ab - 2a^2 + 5a 2p2−23p−162p^2 - \dfrac{2}{3}p - \dfrac{1}{6}
  19. 19将多项式mn2+2mn+mmn^{2}+2mn+m因式分解的结果是 ___ ．
  20. 20In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  21. 21已知aa，bb均为正数，且a≠ba≠b，比较a3+b3a^{3}+b^{3}与a2b+ab2a^{2}b+ab^{2}的大小.
  22. 22下列变形正确的是()(\quad) A. 若3x−1=2x+13x-1=2x+1，则3x+2x=1+13x+2x=1+1 B. 若3(x+1)−5(1−x)=03\left({x+1}\right)-5\left({1-x}\right)=0，则3x+3−5−5x=03x+3-5-5x=0…
  23. 23如果x−(5+2y)=15x-(5+2y)=15，那么2x−4y2x-4y的值是()(\quad) A. 2020 B. 3030 C. 4040 D. −10-10
  24. 24若1a−1b=4 \dfrac {1}{a}- \dfrac {1}{b}=4，则a−2ab−b2a+7ab−2b \dfrac {a-2ab-b}{2a+7ab-2b}的值是 ___ ．
  25. 25下列方程的变形正确的是( ) A. 将方程x−23−1=x+52\dfrac{x-2}{3}-1=\dfrac{x+5}{2}去分母，得2(x−2)−1=3(x+5)2(x-2)-1=3(x+5) B. 将方程3(x−5)−4(x−1)=33(x-5)-4(x-1)=3去括号，得3x−15−4x−4=33x-15-4x-4=3…
  26. 26下面去括号中错误的是（ ） A. a+（b-c）=a+b-c B. a-（b+c-d）=a-b-c-d C. m+2（p-q）=m+2p-2q D. x-3（y+z）=x-3y-3z
  27. 27Express −x2+4x+12-x^2+4x+12 in the form −(x+p)(x−q)-(x+p)(x-q). Answer ... Sketch the graph of y=−x2+4x+12y=-x^2+4x+12 on the axes below. Indicat…
  28. 28Solve the equation 3−2x7=13(2x−1).\displaystyle \frac{3-2x}{7} = \frac{1}{3}(2x-1). Answer x = ... Simplify 25a2−9b215a−10ab+6b2−9b\displaystyle \frac{25a^{2}-9b^{2}}{15a-10ab+6b^{2}-9b}…
  29. 29因式分解：3a2−6a=3a^{2}-6a= ___ ．
  30. 30Solve x/5+(2x−3)/4=−6x/5 + (2x-3)/4 = -6. Answer x = ... Simplify 2(p−3q)/(10r)+(3q−p)2/r2(p-3q)/(10r) + (3q-p)^2/r. Answer ... Solve the inequality x+1≤7x−24<5x+195x+1 \le \dfrac{7x-2}{4} < \dfrac{5x+19}{5}…
  31. 31解方程：1−x3−x=3−x+22.\dfrac{1-x}{3}-x=3-\dfrac{x+2}{2}.
  32. 32Factorise a3−2a2b−4a+8b.a^3 - 2a^2b - 4a + 8b. Solve 3x+29x=17x−3.\dfrac{3x+2}{9x} = \dfrac{1}{7x-3}.
  33. 33Solve the inequality −3x+42<5−x7\frac{-3x+4}{2} < \frac{5-x}{7}. Answer ... Simplify (64a6b−15)−13\left(\dfrac{64a^{6}}{b^{-15}}\right)^{-\tfrac{1}{3}}…
  34. 34分解因式a2−9aa^{2}-9a的结果是 ___ ．
  35. 35将(5x−2)−2(3x−1)(5x-2)-2(3x-1)去括号正确的是()(\quad) A. 5x−2−6x+15x-2-6x+1 B. 5x−2−6x−15x-2-6x-1 C. 5x−2−6x+25x-2-6x+2 D. 5x−2−6x−25x-2-6x-2
  36. 36已知x=1x=1是方程x2−5ax+a2=0x^{2}-5ax+a^{2}=0的一个根，求代数式3a2−15a−73a^{2}-15a-7的值．
  37. 37Factorise completely. 24a2b+12ab2−ab24a^2b + 12ab^2 - ab Answer ... mn−18−9m+2nmn - 18 - 9m + 2n Answer ... Expand and simplify (−2x+3q)(x−2q)(-2x+3q)(x-2q)…
  38. 38计算12a2−9+23−a\dfrac{12}{{{a}^{2}}-9}+\dfrac{2}{3-a}的结果是___.
  39. 39解方程2(5x−1)2=3(5x−1)2(5x-1)^{2}=3(5x-1)的最适当的方法是()(\quad) A. 直接开平方法 B. 配方法 C. 公式法 D. 因式分解法
  40. 40先化简，再求值：5xy−(2x2−xy)+2(x2+3)5xy-(2x^{2}-xy)+2(x^{2}+3)，其中x=1x=1，y=−2y=-2．
  41. 41Write down, and simplify the terms in the expansion of (2+x)5(2 + x)^5 in ascending powers of xx. Hence find the coefficien…
  42. 42Show that (3n+1)2+2(3n + 1)^2 + 2 is always divisible by 3 for all integer values of nn. Answer
  43. 43Given that 21003+21000=2n×3m2^{1003} + 2^{1000} = 2^n \times 3^m, find the value of mm and of nn. Ans: m = ___, n = ___
  44. 44化简：-2（y+x）-（5x-2y）
  45. 45把下列方程改写成用含xx的式子表示yy的形式： (1)32x+2y=1(1)\dfrac{{3}}{{2}}x+{2}y={1}； (2)14x+74y=2(2)\dfrac{{1}}{{4}}x+\dfrac{{7}}{{4}}y={2}； (3)5x−3y=x+2y(3)5x-3y=x+2y…
  46. 46Express x2−6x−2x^2-6x-2 in the form (x−a)2+b(x-a)^2 + b where aa and bb are constants. Answer ___ Hence, state the minimum value…
  47. 47Expand and simplify (3x−y)(y+x).(3x - y)(y + x). Factorise completely 3−12a23 - 12a^2.
  48. 48Solve the inequality 3x+13<2−5x4\frac{3x+1}{3} < \frac{2-5x}{4}. Answer ... It is given that a=2b−3cb+2ca = \frac{2b-3c}{b+2c}. Find aa w…
  49. 49推理是数学的基本思维方式，若推理过程不严谨，则推理结果可能产生错误． 例如，有人声称可以证明“任意一个实数都等于00”，并证明如下： 设任意一个实数为xx，令x=mx=m， 等式两边都乘以xx，得x2=mx.x^{2}=mx.…
  50. 50若M=x3−3x2y+2xy2+3y3M=x^{3}-3x^{2}y+2xy^{2}+3y^{3}，N=x3−2x2y+xy2−5y3N=x^{3}-2x^{2}y+xy^{2}-5y^{3}，则2x3−7x2y+5xy2+14y32x^{3}-7x^{2}y+5xy^{2}+14y^{3}的值为().(\quad).…
  51. 51Factorise 5xy−20y5xy-20y. Answer ... Use set notation to describe the shaded region. Answer ... On the Venn diagram, shade th…
  52. 52Factorise a2b4−ab2.Answer...Expandandsimplifya^2b^4 - ab^2. Answer ... Expand and simplify (3x + 2)^2 + 4x(2 - x). Answer ...
  53. 53Factorise a4−b2a^4 - b^2. Answer ... Factorise completely 8xy−1−4x+2y8xy - 1 - 4x + 2y. Answer ...
  54. 54如果x=−2x=-2，y=12y=\dfrac{1}{2}，那么代数式(4x2−3xy)−3(x2−13xy)(4x^{2}-3xy)-3(x^{2}-\dfrac{1}{3}xy)的值是 ___ .
  55. 55已知aa，bb，cc为△ABC\triangle ABC的三条边的长，当b2+2ab=c2+2acb^{2}+2ab=c^{2}+2ac时， (1)试判断△ABC\triangle ABC属于哪一类三角形； (2)若a=4a=4，b=3b=3…
  56. 56画出曲线 y=x3−4xy = x^3 - 4x 的草图，标出零点、极值点和拐点坐标。
  57. 57Factorise 3x2−14x−53x^2-14x-5. Answer ... Hence, factorise completely 3(y+1)2−14y−193(y+1)^2-14y-19. Answer ...
  58. 58不改变式子a-（b-3c）的值，把其中的括号前的符号变成相反的符号，结果是 ．
  59. 59已知a，b，c都是质数，且满足abc+a=851，则a+b+c的值为 ．
  60. 60已知a=5−1a= \sqrt {5}-1，则2a3+7a2−2a−122a^{3}+7a^{2}-2a-12的值等于 ___ ．