Solutions to Try Its

1. $\left({b}^{2}-a\right)\left(x+6\right)$

2. $\left(x - 6\right)\left(x - 1\right)$

3. a. $\left(2x+3\right)\left(x+3\right)$
b. $\left(3x - 1\right)\left(2x+1\right)$

4. ${\left(7x - 1\right)}^{2}$

5. $\left(9y+10\right)\left(9y - 10\right)$

6. $\left(6a+b\right)\left(36{a}^{2}-6ab+{b}^{2}\right)$

7. $\left(10x - 1\right)\left(100{x}^{2}+10x+1\right)$

8. ${\left(5a - 1\right)}^{-\frac{1}{4}}\left(17a - 2\right)$

Solutions to Odd-Numbered Exercises

1. The terms of a polynomial do not have to have a common factor for the entire polynomial to be factorable. For example, $4{x}^{2}$ and $-9{y}^{2}$ don’t have a common factor, but the whole polynomial is still factorable: $4{x}^{2}-9{y}^{2}=\left(2x+3y\right)\left(2x - 3y\right)$.

3. Divide the $x$ term into the sum of two terms, factor each portion of the expression separately, and then factor out the GCF of the entire expression.

5. $7m$

7. $10{m}^{3}$

9. $y$

11. $\left(2a - 3\right)\left(a+6\right)$

13. $\left(3n - 11\right)\left(2n+1\right)$

15. $\left(p+1\right)\left(2p - 7\right)$

17. $\left(5h+3\right)\left(2h - 3\right)$

19. $\left(9d - 1\right)\left(d - 8\right)$

21. $\left(12t+13\right)\left(t - 1\right)$

23. $\left(4x+10\right)\left(4x - 10\right)$

25. $\left(11p+13\right)\left(11p - 13\right)$

27. $\left(19d+9\right)\left(19d - 9\right)$

29. $\left(12b+5c\right)\left(12b - 5c\right)$

31. ${\left(7n+12\right)}^{2}$

33. ${\left(15y+4\right)}^{2}$

35. ${\left(5p - 12\right)}^{2}$

37. $\left(x+6\right)\left({x}^{2}-6x+36\right)$

39. $\left(5a+7\right)\left(25{a}^{2}-35a+49\right)$

41. $\left(4x - 5\right)\left(16{x}^{2}+20x+25\right)$

43. $\left(5r+12s\right)\left(25{r}^{2}-60rs+144{s}^{2}\right)$

45. ${\left(2c+3\right)}^{-\frac{1}{4}}\left(-7c - 15\right)$

47. ${\left(x+2\right)}^{-\frac{2}{5}}\left(19x+10\right)$

49. ${\left(2z - 9\right)}^{-\frac{3}{2}}\left(27z - 99\right)$

51. $\left(14x - 3\right)\left(7x+9\right)$

53. $\left(3x+5\right)\left(3x - 5\right)$

55. ${\left(2x+5\right)}^{2}{\left(2x - 5\right)}^{2}$

57. $\left(4{z}^{2}+49{a}^{2}\right)\left(2z+7a\right)\left(2z - 7a\right)$

59. $\frac{1}{\left(4x+9\right)\left(4x - 9\right)\left(2x+3\right)}$