CAPITULO X
Descomposición Factorial
Descomposición Factorial
- Ejercicio 92
Factorar o descomponer en dos factores:
- a 2 –2ab+ b 2 = ( a–b ) 2
- a 2 +2ab+ b 2 = ( a+b ) 2
- x 2 –2x+1= ( x–1 ) 2
- y 4 +1+2 y 2 = y 4 +2 y 2 +1 = ( y 2 +1 ) 2
- a 2 –10a+25= ( a–5 ) 2
- 9–6x+ x 2 = ( 3–x ) 2
- 16+40 x 2 +25 x 4 = ( 4+5 x 2 ) 2
- 1+49 a 2 –14a =49 a 2 –14a+1 = ( 7a–1 ) 2
- 36+12 m 2 + m 4 = ( 6+ m 2 ) 2
- 1–2 a 3 + a 6 = ( 1– a 3 ) 2
- a 8 +18 a 4 +81= ( a 4 +9 ) 2
- a 6 –2 a 3 b 3 + b 6 = ( a 3 – b 3 ) 2
- 4 x 2 –12xy+9 y 2 = ( 2x–3y ) 2
- 9 b 2 –30 a 2 b+25 a 4 = ( 3b–5 a 2 ) 2
- 1+14 x 2 y+49 x 4 y 2 = ( 1+7 x 2 y ) 2
- 1+ a 10 –2 a 5 =1–2 a 5 + a 10 = ( 1– a 5 ) 2
- 49 m 6 –70a m 3 n 2 +25 a 2 n 4 = ( 7 m 3 –5a n 2 ) 2
- 100 x 10 –60 a 4 x 5 y 6 +9 a 8 y 12 = ( 10 x 5 –3 a 4 y 6 ) 2
- 121+198 x 6 +81 x 12 = ( 11+9 x 6 ) 2
- a 2 –24a m 2 x 2 +144 m 4 x 4 = ( a–12 m 2 x 2 ) 2
- 16–104 x 2 +169 x 4 = ( 4–13 x 2 ) 2
- 400 x 10 +40 x 5 +1= ( 20 x 5 +1 ) 2
- a 2 4 –ab+ b 2 = ( a 2 –b ) 2
- 1+ 2b 3 + b 2 9 = ( 1+ b 3 ) 2
- a 4 – a 2 b 2 + b 4 4 = ( a 2 – b 2 2 ) 2
- 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
- 16 x 6 –2 x 3 y 2 + y 4 16 = ( 4 x 3 – y 2 4 ) 2
- n 2 9 +2mn+9 m 2 = ( n 3 +3m ) 2
- a 2 +2a( a+b ) + ( a+b ) 2 = [ a+( a+b ) ] 2 =( a+a+b ) = ( 2a+b ) 2
- 4–4( 1–a ) + ( 1–a ) 2 = [ 2–( 1–a ) ] 2 = ( 2–1+a ) 2 = ( 1+a ) 2
- 4 m 2 –4m( n–m ) + ( n–m ) 2 = [ 2m–( n–m ) ] 2 = ( 2m–n+m ) 2 = ( 3m–n ) 2
- ( m–n ) 2 +6( m–n ) +9 = [ ( m–n ) +3 ] 2 = ( m–n+3 ) 2
- ( a+x ) 2 –2( a+x ) ( x+y ) + ( x+y ) 2 = [ ( a+x ) –( x+y ) ] 2 = ( a+ x – x –y ) 2 = ( a–y ) 2
- ( 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
- 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
- 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