Now transition from multiplying special products to factoring special products. If you can recognize them, you can save a lot of time. The following is a list of these special products (note that a² + b² cannot be factored):

[latex]\begin{array}{lll} a^2-b^2&=&(a+b)(a-b) \\ (a+b)^2&=&a^2+2ab+b^2 \\ (a-b)^2&=&a^2-2ab+b^2 \\ a^3-b^3&=&(a-b)(a^2+ab+b^2) \\ a^3+b^3&=&(a+b)(a^2-ab+b^2) \\ \end{array}[/latex]

The challenge is therefore in recognizing the special product.

Questions

Factor each of the following polynomials.

1. [latex]r^2-16[/latex]
2. [latex]x^2-9[/latex]
3. [latex]v^2-25[/latex]
4. [latex]x^2-1[/latex]
5. [latex]p^2-4[/latex]
6. [latex]4v^2-1[/latex]
7. [latex]3x^2-27[/latex]
8. [latex]5n^2-20[/latex]
9. [latex]16x^2-36[/latex]
10. [latex]125x^2+45y^2[/latex]
11. [latex]a^2-2a+1[/latex]
12. [latex]k^2+4k+4[/latex]
13. [latex]x^2+6x+9[/latex]
14. [latex]n^2-8n+16[/latex]
15. [latex]25p^2-10p+1[/latex]
16. [latex]x^2+2x+1[/latex]
17. [latex]25a^2+30ab+9b^2[/latex]
18. [latex]x^2+8xy+16y^2[/latex]
19. [latex]8x^2-24xy+18y^2[/latex]
20. [latex]20x^2+20xy+5y^2[/latex]
21. [latex]8-m^3[/latex]
22. [latex]x^3+64[/latex]
23. [latex]x^3-64[/latex]
24. [latex]x^3+8[/latex]
25. [latex]216-u^3[/latex]
26. [latex]125x^3-216[/latex]
27. [latex]125a^3-64[/latex]
28. [latex]64x^3-27[/latex]
29. [latex]64x^3+27y^3[/latex]
30. [latex]32m^3-108n^3[/latex]

Answer Key 7.5