# Ejercicio 71

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CAPITULO VI

PRODUCTOS Y COCIENTES NOTABLES
Ejercicio 71
Hallar, por simple inspección, el cociente de:
1. $\frac{{x}^{4}–{y}^{4}}{x–y}={x}^{3}+{x}^{2}y+x{y}^{2}+{y}^{3}$
2. $\frac{{m}^{5}+{n}^{5}}{m+n}={m}^{4}–{m}^{3}n+{m}^{2}{n}^{2}–m{n}^{3}+{n}^{4}$
3. $\frac{{a}^{5}–{n}^{5}}{a–n}={a}^{4}+{a}^{3}n+{a}^{2}{n}^{2}+a{n}^{3}+{n}^{4}$
4. $\frac{{x}^{6}–{y}^{6}}{x+y}={x}^{5}–{x}^{4}y+{x}^{3}{y}^{2}–{x}^{2}{y}^{3}+x{y}^{4}–{y}^{5}$
5. $\frac{{a}^{6}–{b}^{6}}{a–b}={a}^{5}+{a}^{4}b+{a}^{3}{b}^{2}+{a}^{2}{b}^{3}+a{b}^{4}+{b}^{5}$
6. $\frac{{x}^{7}+{y}^{7}}{x+y}={x}^{6}–{x}^{5}y+{x}^{4}{y}^{2}–{x}^{3}{y}^{3}+{x}^{2}{y}^{4}–x{y}^{5}+{y}^{6}$
7. $\frac{{a}^{7}–{m}^{7}}{a–m}={a}^{6}+a{m}^{5}+{a}^{2}{m}^{4}+{a}^{3}{m}^{3}+{a}^{2}{m}^{4}+a{m}^{5}+{m}^{6}$
8. $\frac{{a}^{8}–{b}^{8}}{a+b}={a}^{7}–{a}^{6}b+{a}^{5}{b}^{2}–{a}^{4}{b}^{3}+{a}^{3}{b}^{4}–{a}^{2}{b}^{5}+a{b}^{6}–{b}^{7}$
9. $\frac{{x}^{10}–{y}^{10}}{x–y}={x}^{9}+{x}^{8}y+{x}^{7}{y}^{2}+{x}^{6}{y}^{3}+{x}^{5}{y}^{4}+{x}^{4}{y}^{5}+{x}^{3}{y}^{6}+{x}^{2}{y}^{7}+x{y}^{8}+{y}^{9}$
10. $\frac{{m}^{9}+{n}^{9}}{m+n}={m}^{8}–{m}^{7}n+{m}^{6}{n}^{2}–{m}^{5}{n}^{3}+{m}^{4}{n}^{4}–{m}^{3}{n}^{5}+{m}^{2}{n}^{6}–m{n}^{7}+{n}^{8}$
11. $\frac{{m}^{9}–{n}^{9}}{m–n}={m}^{8}+{m}^{7}n+{m}^{6}{n}^{2}+{m}^{5}{n}^{3}+{m}^{4}{n}^{4}+{m}^{3}{n}^{5}+{m}^{2}{n}^{6}+m{n}^{7}+{n}^{8}$
12. $\frac{{a}^{10}–{x}^{10}}{a+x}={a}^{9}–{a}^{8}x+{a}^{7}{x}^{2}–{a}^{6}{x}^{3}+{a}^{5}{x}^{4}–{a}^{4}{x}^{5}+{a}^{3}{x}^{6}–{a}^{2}{x}^{7}+a{x}^{8}–{x}^{9}$
13. $\frac{1–{n}^{5}}{1–n}=1+n+{n}^{2}+{n}^{3}+{n}^{4}$
14. $\frac{1–{a}^{6}}{1–a}=1+a+{a}^{2}+{a}^{3}+{a}^{5}$
15. $\frac{1+{a}^{7}}{1+a}=1–a+{a}^{2}–{a}^{3}+{a}^{4}–{a}^{5}+{a}^{6}$
16. $\frac{1–{m}^{8}}{1+m}=1–m+{m}^{2}–{m}^{3}+{m}^{4}–{m}^{5}+{m}^{6}–{m}^{7}$
17. $\frac{{x}^{4}–16}{x–2}={x}^{3}+2{x}^{2}+4x+8$
18. $\frac{{x}^{6}–64}{x+2}={x}^{5}–2{x}^{4}+4{x}^{3}–8{x}^{2}+16x–32$
19. $\frac{{x}^{7}–128}{x–2}={x}^{6}+2{x}^{5}+4{x}^{4}+8{x}^{3}+16{x}^{2}+32x+64$
20. $\frac{{a}^{5}+243}{a+3}={a}^{4}–3{a}^{3}+9{a}^{2}–27a+81$
21. $\frac{{x}^{6}–729}{x–3}={x}^{5}+3{x}^{4}+9{x}^{3}+27{x}^{2}+81x+243$
22. $\frac{625–{x}^{4}}{x+5}=125–25x+5{x}^{2}–{x}^{3}$
23. $\frac{{m}^{8}–256}{m–2}={m}^{7}+2{m}^{6}+4{m}^{5}+8{m}^{4}+16{m}^{3}+32{m}^{2}+64m+128$
24. $\frac{{x}^{10}–1}{x–1}={x}^{9}+{x}^{8}+{x}^{7}+{x}^{6}+{x}^{5}+{x}^{4}+{x}^{3}+{x}^{2}+x+1$
25. $\frac{{x}^{5}+243{y}^{5}}{x+3y}={x}^{4}–3{x}^{3}y+9{x}^{2}{y}^{2}–27x{y}^{3}+81{y}^{4}$
26. $\frac{16{a}^{4}–81{b}^{4}}{2a–3b}=8{a}^{3}+12{a}^{2}b+18a{b}^{2}+27{b}^{3}$
27. $\frac{64{m}^{6}–729{n}^{6}}{2m+3n}=32{m}^{5}–48{m}^{4}n+72{m}^{3}{n}^{2}–108{m}^{2}{n}^{3}+162m{n}^{4}–243{n}^{5}$
28. $\frac{1024{x}^{10}–1}{2x–1}=512{x}^{9}+256{x}^{8}+128{x}^{7}+64{x}^{6}+32{x}^{5}+16{x}^{4}+8{x}^{3}+4{x}^{2}+2x+1$
29. $\frac{512{a}^{9}+{b}^{9}}{2a+b}=256{a}^{8}–128{a}^{7}b+64{a}^{6}{b}^{2}–32{a}^{5}{b}^{3}+16{a}^{4}{b}^{4}–8{a}^{3}{b}^{5}+4{a}^{2}{b}^{6}–2a{b}^{7}+{b}^{8}$
30. $\frac{{a}^{6}–729}{a–3}={a}^{5}+3{a}^{4}+9{a}^{3}+27{a}^{2}+81a+243$