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CAPITULO X

Descomposición Factorial
Ejercicio 92
Factorar o descomponer en dos factores:
  1. a 2 –2ab+ b 2 = (a–b ) 2
  2. a 2 +2ab+ b 2 = (a+b ) 2
  3. x 2 –2x+1= (x–1 ) 2
  4. y 4 +1+2 y 2 = y 4 +2 y 2 +1 = ( y 2 +1 ) 2
  5. a 2 –10a+25= (a–5 ) 2
  6. 9–6x+ x 2 = (3–x ) 2
  7. 16+40 x 2 +25 x 4 = (4+5 x 2 ) 2
  8. 1+49 a 2 –14a =49 a 2 –14a+1 = (7a–1 ) 2
  9. 36+12 m 2 + m 4 = (6+ m 2 ) 2
  10. 1–2 a 3 + a 6 = (1– a 3 ) 2
  11. a 8 +18 a 4 +81= ( a 4 +9 ) 2
  12. a 6 –2 a 3 b 3 + b 6 = ( a 3 – b 3 ) 2
  13. 4 x 2 –12xy+9 y 2 = (2x–3y ) 2
  14. 9 b 2 –30 a 2 b+25 a 4 = (3b–5 a 2 ) 2
  15. 1+14 x 2 y+49 x 4 y 2 = (1+7 x 2 y ) 2
  16. 1+ a 10 –2 a 5 =1–2 a 5 + a 10 = (1– a 5 ) 2
  17. 49 m 6 –70a m 3 n 2 +25 a 2 n 4 = (7 m 3 –5a n 2 ) 2
  18. 100 x 10 –60 a 4 x 5 y 6 +9 a 8 y 12 = (10 x 5 –3 a 4 y 6 ) 2
  19. 121+198 x 6 +81 x 12 = (11+9 x 6 ) 2
  20. a 2 –24a m 2 x 2 +144 m 4 x 4 = (a–12 m 2 x 2 ) 2
  21. 16–104 x 2 +169 x 4 = (4–13 x 2 ) 2
  22. 400 x 10 +40 x 5 +1= (20 x 5 +1 ) 2
  23. a 2 4 –ab+ b 2 = ( a 2 –b ) 2
  24. 1+ 2b 3 + b 2 9 = (1+ b 3 ) 2
  25. a 4 – a 2 b 2 + b 4 4 = ( a 2 – b 2 2 ) 2
  26. 1 25 + 25 x 4 36 – x 2 3 = 1 25 – x 2 3 + 25 x 4 36 = ( 1 5 – 5 x 2 6 ) 2
  27. 16 x 6 –2 x 3 y 2 + y 4 16 = (4 x 3 – y 2 4 ) 2
  28. n 2 9 +2mn+9 m 2 = ( n 3 +3m ) 2
  29. a 2 +2a(a+b ) + (a+b ) 2 = [a+(a+b ) ] 2 =(a+a+b ) = (2a+b ) 2
  30. 4–4(1–a ) + (1–a ) 2 = [2–(1–a ) ] 2 = (2–1+a ) 2 = (1+a ) 2
  31. 4 m 2 –4m(n–m ) + (n–m ) 2 = [2m–(n–m ) ] 2 = (2m–n+m ) 2 = (3m–n ) 2
  32. (m–n ) 2 +6(m–n ) +9 = [(m–n ) +3 ] 2 = (m–n+3 ) 2
  33. (a+x ) 2 –2(a+x ) (x+y ) + (x+y ) 2 = [(a+x ) –(x+y ) ] 2 = (a+ x – x –y ) 2 = (a–y ) 2
  34. (m+n ) 2 –2(a–m ) (m+n ) + (a–m ) 2 = [(m+n ) –(a–m ) ] 2 = (m+n–a+m ) 2 = (2m+n–a ) 2
  35. 4 (1+a ) 2 –4(1+a ) (b–1 ) + (b–1 ) 2 = [2(1+a ) –(b–1 ) ] 2 = (2+2a–b+1 ) 2 = (2a–b+3 ) 2
  36. 9 (x–y ) 2 +12(x–y ) (x+y ) +4 (x+y ) 2 = [3(x–y ) +2(x+y ) ] 2 = (3x–3y+2x+2y ) 2 = (5x–y ) 2
Categories: Capítulo X