Math topic中文

Factorisation linear

factorisation of linear expressions of the form ax+bx+kay+kbyax + bx + kay + kby

Practice questions

  1. 1Factorise completely. abc−3c−6+2ababc - 3c - 6 + 2ab Answer ... 80x4−580x^{4} - 5 Answer ...
  2. 2Factorise the following completely. 45b−18ab−2a2+5a45b - 18ab - 2a^2 + 5a 2p2−23p−162p^2 - \dfrac{2}{3}p - \dfrac{1}{6}
  3. 3Solve 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}…
  4. 4Factorise a3−2a2b−4a+8b.a^3 - 2a^2b - 4a + 8b. Solve 3x+29x=17x−3.\dfrac{3x+2}{9x} = \dfrac{1}{7x-3}.
  5. 5Solve 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}}…
  6. 6Factorise 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)…
  7. 7Factorise a2b4−ab2.Answer...Expandandsimplifya^2b^4 - ab^2. Answer ... Expand and simplify (3x + 2)^2 + 4x(2 - x). Answer ...
  8. 8Factorise a4−b2a^4 - b^2. Answer ... Factorise completely 8xy−1−4x+2y8xy - 1 - 4x + 2y. Answer ...
  9. 9Factorise 4ax2−4ay2+2bx2−2by24ax^2 - 4ay^2 + 2bx^2 - 2by^2 completely.
  10. 10Write as a single fraction in its simplest form. 3t2w⋅9t2w3\dfrac{3t^2}{w} \cdot \dfrac{9t^2}{w^3} Answer ----------------------…
  11. 11Factorise completely 2x3−13x2+6x2x^3 - 13x^2 + 6x. Answer ...
  12. 12Factorise completely the expressions. 4(x−y)2−9(x+y)24(x - y)^2 - 9(x + y)^2 10ax+15ay−8bx−12by10ax + 15ay - 8bx - 12by
  13. 13Factorise completely 2p4−32s42p^4 - 32s^4, Answer ... 12cd−9cx+6xy−8dy12cd - 9cx + 6xy - 8dy. Answer ...
  14. 14分解因式：am+an+bm+bn= ．
  15. 15Factorise completely 4mn−16n2−4m2n+64n34mn - 16n^2 - 4m^2n + 64n^3. Answer ...
  16. 16Factorise completely 5pr−2ps−5qr+2qs5pr - 2ps - 5qr + 2qs. Given that p≠qp \neq q, find the value of rs\frac{r}{s} when 5pr−2ps−5qr+2qs=05pr - 2ps - 5qr + 2qs = 0…
  17. 17Simplify −4(2a+b)+7(b−3a)-4(2a + b) + 7(b - 3a). Factorise completely 12xy+6x2−2y−x12xy + 6x^2 - 2y - x.
  18. 18Factorise 6a−15a2+20ab−8b25a3−4a\dfrac{6a-15a^2+20ab-8b}{25a^3-4a} completely.
  19. 19Expand and simplify 2x−3(2x−5).2x-3(2x-5). Answer ___ Factorise completely x2−y2−2x+2yx^{2}-y^{2}-2x+2y. Answer ___
  20. 20Simplify 2x2+4xy−3x−6y2x2+xy−6y2\dfrac{2x^2+4xy-3x-6y}{2x^2+xy-6y^2}. Answer ...
  21. 21Expand and simplify 2(5m+3n)22(5m+3n)^2. Factorise completely 24(mn)2−21mn324(mn)^2 - 21mn^3.
  22. 22Simplify -9(5x+2y)-3(2x-y). Answer ___ Factorise completely 6ap+9aq-12bq-8bp. Answer ___
  23. 23Factorize completely, x2y4−z6x^{2}y^{4} - z^{6} Answer ___ 15a^{2} - 6a + 20ab - 8b Answer ___
  24. 24Explain why (5n+2)2−(5n−2)2(5n+2)^2-(5n-2)^2 is a multiple of 8 for all integer values of n. Answer ...
  25. 25Simplify 5a36b+2ab4a2b\frac{5a^3}{6b} + \frac{2ab}{4a^2b}. Solve x8=50x\frac{x}{8} = \frac{50}{x}. Simplify 4v2−12pv+p−10v−5\frac{4v^2 - 1}{2pv + p - 10v - 5}…