Ejercicio 133

Ejercicio 133

1. ( a+ a b ) ( a– a b+1 ) =( ab+a b ) [ a( b+1 ) –a b+1 ] = a ( b+1 ) b ( ab+ a – a b+1 ) = a 2 b b = a 2
2. ( x– 2 x+1 ) ( x+ 1 x+2 ) =[ x( x+1 ) –2 x+1 ] [ x( x+2 ) +1 x+2 ] =[ x 2 +x–2 x+1 ] [ x 2 +2x+1 x+2 ] = ( x+2 ) ( x–1 ) x+1 ( x+1 ) 2 x+2 = x 2 –1
3. ( 1– x a+x ) ( 1+ x a ) =[ a+ x – x a+x ] [ a+x a ] = a a =1
4. ( a+ ab a–b ) ( 1– b 2 a 2 ) =[ a( a–b ) +ab a–b ] [ a 2 – b 2 a 2 ] =[ a 2 – ab + ab a–b ] ( a+b ) ( a–b ) a 2 = a 2 ( a+b ) a 2 =a+b
5. ( x+2– 12 x+1 ) ( x–2+ 10–3x x+5 ) =[ ( x+1 ) ( x+2 ) –12 x+1 ] [ ( x–2 ) ( x+5 ) +10–3x x+5 ] =[ x 2 +3x+2–12 x+1 ] [ x 2 + 3x – 10 + 10 – 3x x+5 ] =[ x 2 +3x–10 x+1 ] ( x 2 x+5 ) = ( x+5 ) ( x–2 ) x+1 ( x 2 x+5 ) = x 2 ( x–2 ) x+1
6. ( 1+ x y ) ( x– x 2 x+y ) =( y+x y ) [ x( x+y ) – x 2 x+y ] =( 1 y ) [ x 2 +xy– x 2 x+y ] = x y y =x
7. ( a+x– ax+ x 2 a+2x ) ( 1+ x a+x ) =[ ( a+x ) ( a+2x ) –( ax+ x 2 ) a+2x ] [ a+x+x a+x ] =[ a 2 +2ax+ ax +2 x 2 – ax – x 2 a+2x ] [ a+2x a+x ] =( a 2 +2ax+ x 2 ) ( 1 a+x ) = ( a+x ) 2 ( 1 a+x ) =a+x
8. ( x– x 3 –6x x 2 –25 ) ( x+1– 8 x+3 ) =[ x( x 2 –25 ) –( x 3 –6x ) x 2 –25 ] [ ( x+1 ) ( x+3 ) –8 x+3 ] =[ x 3 –25x– x 3 +6x x 2 –25 ] [ x 2 +4x+3–8 x+3 ] =( –19x x 2 –25 ) ( x 2 +4x–5 x+3 ) =[ –19x ( x–5 ) ( x+5 ) ] [ ( x+5 ) ( x–1 ) x+3 ] = 19x–19 x 2 ( x–5 ) ( x+3 )
9. ( m– mn m+n ) ( 1+ n 3 m 3 ) =[ m( m+n ) –mn m+n ] ( m 3 + n 3 m 3 ) =[ m 2 + mn – mn m+n ] [ ( m+n ) ( m 2 –mn+ n 2 ) m 3 ] = m 2 ( m+n ) ( m 2 –mn+ n 2 ) m 3 = m 2 –mn+ n 2 m
10. ( a+2x– 14 x 2 2a+x ) ( a–x+ a 2 +5 x 2 a+4x ) =[ ( a+2x ) ( 2a+x ) –14 x 2 2a+x ] [ ( a–x ) ( a+4x ) + a 2 +5 x 2 a+4x ] =[ 2 a 2 +ax+4ax+2 x 2 –14 x 2 2a+x ] [ a 2 +4ax–ax–4 x 2 + a 2 +5 x 2 a+4x ] =[ 2 a 2 +5ax–12 x 2 2a+x ] [ 2 a 2 +3ax+ x 2 a+4x ] =[ 2 a 2 –3ax+8ax–12 x 2 2a+x ] [ 2 a 2 +2ax+ax+ x 2 a+4x ] =[ a( 2a–3x ) +4x( 2a–3x ) 2a+x ] [ 2a( a+x ) +x( a+x ) a+4x ] = ( a+4x ) ( 2a–3x ) 2a+x × ( 2a+x ) ( a+x ) a+4x =( 2a–3x ) ( a+x )
11. ( 1+ a b ) ( 1– b a ) ( 1+ b 2 a 2 – b 2 ) =( b+a b ) ( a–b a ) [ a 2 – b 2 + b 2 ( a–b ) ( a+b ) ] = a 2 a b = a b
12. ( 2+ 2 x+1 ) ( 3– 6 x+2 ) ( 1+ 1 x ) =[ 2( x+1 ) +2 x+1 ] [ 3( x+2 ) –6 x+2 ] ( x+1 x ) =( 2x+4 ) [ 3x+ 6 – 6 x+2 ] ( 1 x ) =2 ( x+2 ) ( 3 x x+2 ) ( 1 x ) =6