# POLQ 2 | Lesson 1 | Making Connections (Factoring with Symbols) Solutions

Solutions for the Factoring with Symbols practice:

(SPECIAL FACTORING PATTERNS NOTED)

1.  $$(\#-!)(\#+!)$$  Difference of Squares
2. $$(\#+4) (\#-7)$$
3. $$(@+3)^2$$ Perfect Square Trinomial
4.  $$(∂+2) (3∂ +2)$$
5.  $$(F(x) – 4)(F(x) + 2)$$
6.  $$(\sin x – \cos x) (\sin x +\cos x)$$ Difference of Squares
7. $$(\sec B – \cos B) (\sec B^2 +\sec B \cos B +\cos B^2)$$
8. $$8((a – 3)- 4)^2$$  Perfect Square Trinomial
9. $$(\cos t -\sin t)(\cos t + \sin t)(\cos t^2+ \sin t^2)$$  Difference of Squares
10. $$(F(x) – 1)(F(x) + 1)$$  Difference of Squares
11. $$(Ω – 1)(Ω + 1)$$ Difference of Squares
12. $$\&(\& + %)$$
13. $$(4x + 1)(x – 1)$$
14. $$((x + 3) – 1)((x + 3 )+ 8)$$
15. $$\tan t(\tan t – 5)$$
16. $$(96-)(96+)$$  Difference of Two Squares
17.  $$( ◊-Θ )(◊^2 + ◊Θ +Θ ^2)$$  Difference of Cubes
18. $$((y-1)+ (x+2))( (y-1) – (x+2))$$ Difference of Squares
19.  $$((x-3) +3)((x-3)-3)$$  Difference of Squares
20.  $$((3x+9) +3)((3x+9)-3)$$ Difference of Squares
21.   $$(+1) (-1)$$ Difference of Squares
22. $$((x+ 1) – 4)^2$$ Perfect Square Trinomial
23. $$(\& – 9)(\& + 3)$$
24. $$4(48^2 -74 -399)$$
25. $$((Θ + 1) – 7)((Θ + 1) + 4)$$
26. $$(a + 2)((a+ 2) – 1)((a + 2) + 1)$$ Difference of Squares
27. $$(y – 1)^2((y – 1)^2 – 5)$$
28. $$(\sin A + \cos A)(\sin A^2 – \sin A \cos A + \cos A^2)$$ Sum of Cubes
29. $$(\sin x + \cos x)-(\sin x + \tan x))((\sin x + \cos x)+ (\sin x + \tan x))$$ Difference of Squares
30. $$(θ^2 +Θ^2)(θ- Θ)(θ+Θ)$$ Difference of Squares