Вопрос:

Представьте в виде произведения многочлен: 1) $$x^2-36$$; 2) $$1-a^2$$; 3) $$16-x^2$$; 4) $$-y^2 +81$$; 5) $$\frac{1}{9}-b^2$$; 6) $$y^2 - \frac{25}{36}$$; 7) $$0,81-x^2$$; 8) $$16a^2-1$$; 9) $$100-9y^2$$; 10) $$36a^2-25b^2$$; 11) $$-9p^2 +0,16q^2$$; 12) $$\frac{4}{81}k^2-\frac{1}{25}b^2$$; 13) $$7\frac{1}{9}n^2-4m^2$$; 14) $$0,04x^2 -0,64y^2$$; 15) $$9m^2n^2-1$$; 16) $$81-16p^2q^2$$; 17) $$0,01a^2b^2-100m^2$$; 18) $$121a^2b^4-49c^2$$; 19) $$9x^4z^2-0,09y^2$$; 20) $$-\frac{9}{64}t^2 +36k^4l^6$$

Ответ:

Решение заданий

  1. $$x^2 - 36 = (x - 6)(x + 6)$$
  2. $$1 - a^2 = (1 - a)(1 + a)$$
  3. $$16 - x^2 = (4 - x)(4 + x)$$
  4. $$-y^2 + 81 = 81 - y^2 = (9 - y)(9 + y)$$
  5. $$\frac{1}{9} - b^2 = (\frac{1}{3} - b)(\frac{1}{3} + b)$$
  6. $$y^2 - \frac{25}{36} = (y - \frac{5}{6})(y + \frac{5}{6})$$
  7. $$0.81 - x^2 = (0.9 - x)(0.9 + x)$$
  8. $$16a^2 - 1 = (4a - 1)(4a + 1)$$
  9. $$100 - 9y^2 = (10 - 3y)(10 + 3y)$$
  10. $$36a^2 - 25b^2 = (6a - 5b)(6a + 5b)$$
  11. $$-9p^2 + 0.16q^2 = 0.16q^2 - 9p^2 = (0.4q - 3p)(0.4q + 3p)$$
  12. $$\frac{4}{81}k^2 - \frac{1}{25}b^2 = (\frac{2}{9}k - \frac{1}{5}b)(\frac{2}{9}k + \frac{1}{5}b)$$
  13. $$7\frac{1}{9}n^2 - 4m^2 = (\frac{8}{3}n - 2m)(\frac{8}{3}n + 2m)$$
  14. $$0.04x^2 - 0.64y^2 = (0.2x - 0.8y)(0.2x + 0.8y)$$
  15. $$9m^2n^2 - 1 = (3mn - 1)(3mn + 1)$$
  16. $$81 - 16p^2q^2 = (9 - 4pq)(9 + 4pq)$$
  17. $$0.01a^2b^2 - 100m^2 = (0.1ab - 10m)(0.1ab + 10m)$$
  18. $$121a^2b^4 - 49c^2 = (11ab^2 - 7c)(11ab^2 + 7c)$$
  19. $$9x^4z^2 - 0.09y^2 = (3x^2z - 0.3y)(3x^2z + 0.3y)$$
  20. $$-\frac{9}{64}t^2 + 36k^4l^6 = 36k^4l^6 - \frac{9}{64}t^2 = (6k^2l^3 - \frac{3}{8}t)(6k^2l^3 + \frac{3}{8}t)$$
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