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CAPITULO X

Descomposición Factorial
Ejercicio 105
Factorar:
1. ${a}^{5}+1=\left(a+1\right)\left({a}^{4}–{a}^{3}+{a}^{2}–a+1\right)$
2. ${a}^{5}–1=\left(a–1\right)\left({a}^{4}+{a}^{3}+{a}^{2}+a+1\right)$
3. $1–{x}^{5}=\left(1–x\right)\left(1+x+{x}^{2}+{x}^{3}+{x}^{4}\right)$
4. ${a}^{7}+{b}^{7}=\left(a+b\right)\left({a}^{6}–{a}^{5}b+{a}^{4}{b}^{2}–{a}^{3}{b}^{3}+{a}^{2}{b}^{4}–a{b}^{5}+{b}^{6}\right)$
5. ${m}^{7}–{n}^{7}=\left(m–n\right)\left({m}^{6}+{m}^{5}n+{m}^{4}{n}^{2}+{m}^{3}{n}^{3}+{m}^{2}{n}^{4}+m{n}^{5}+{n}^{6}\right)$
6. ${a}^{5}+243=\left(a+3\right)\left({a}^{4}–3{a}^{3}+9{a}^{2}–27a+81\right)$
7. $32–{m}^{5}=\left(2–m\right)\left(16+8m+4{m}^{2}+2{m}^{3}+{m}^{4}\right)$
8. $1+243{x}^{5}=\left(1+3x\right)\left(1–3x+9{x}^{2}–27{x}^{3}+81{x}^{4}\right)$
9. ${x}^{7}+128=\left(x+2\right)\left({x}^{6}–2{x}^{5}+4{x}^{4}–8{x}^{3}+16{x}^{2}–32x+64\right)$
10. $243–32{b}^{5}=\left(3–2b\right)\left(81+54b+36{b}^{2}+24{b}^{3}+16{b}^{4}\right)$
11. ${a}^{5}+{b}^{5}{c}^{5}=\left(a+bc\right)\left({a}^{4}–{a}^{3}bc+{a}^{2}{b}^{2}{c}^{2}–a{b}^{3}{c}^{3}+{b}^{4}{c}^{4}\right)$
12. ${m}^{7}–{a}^{7}{x}^{7}=\left(m–ax\right)\left({m}^{6}+{m}^{5}ax+{m}^{4}{a}^{2}{x}^{2}+{m}^{3}{a}^{3}{x}^{3}+{m}^{2}{a}^{4}{x}^{4}+m{a}^{5}{x}^{5}+{a}^{6}{x}^{6}\right)$
13. $1+{x}^{7}=\left(1+x\right)\left(1–x+{x}^{2}–{x}^{3}+{x}^{4}–{x}^{5}+{x}^{6}\right)$
14. ${x}^{7}–{y}^{7}=\left(x–y\right)\left({x}^{6}+{x}^{5}y+{x}^{4}{y}^{2}+{x}^{3}{y}^{3}+{x}^{2}{y}^{4}+x{y}^{5}+{y}^{6}\right)$
15. ${a}^{7}+2187=\left(a+3\right)\left({a}^{6}–3{a}^{5}+9{a}^{4}–27{a}^{3}+81{a}^{2}–243a+729\right)$
16. $1–128{a}^{7}=\left(1–2a\right)\left(1+2a+4{a}^{2}+8{a}^{3}+16{a}^{4}+32{a}^{5}+64{a}^{6}\right)$
17. ${x}^{10}+32{y}^{5}=\left({x}^{2}+2y\right)\left({x}^{8}–2{x}^{6}y+4{x}^{4}{y}^{2}–8{x}^{2}{y}^{3}+16{y}^{4}\right)$
18. $1+128{x}^{14}=\left(1+2{x}^{2}\right)\left(1–2{x}^{2}+4{x}^{4}–8{x}^{6}+16{x}^{8}–32{x}^{10}+64{x}^{12}\right)$