Comparte esto 👍👍DESCARGACAPITULO X Descomposición Factorial Ejercicio 94Descomponer en dos factores y simplificar, si es posible: (x+y ) 2 – a 2 =[(x+y ) +a ] [(x+y ) –a ] =(x+y+a ) (x+y–a ) 4– (a+1 ) 2 =[2+(a+1 ) ] [2–(a+1 ) ] =(2+a+1 ) (2–a–1 ) =(a+3 ) (1–a ) 9– (m+n ) 2 =[3+(m+n ) ] [3–(m+n ) ] =(3+m+n ) (3–m–n ) (m–n ) 2 –16 =[(m–n ) –4 ] [(m–n ) +4 ] =(m–n–4 ) (m–n+4 ) (x–y ) 2 –4 z 2 =[(x–y ) +2z ] [(x–y ) –2z ] =(x–y+2z ) (x–y–2z ) (a+2b ) 2 –1 =[(a+2b ) –1 ] [(a+2b ) +1 ] =(a+2b–1 ) (a+2b+1 ) 1– (x–2y ) 2 =[1–(x–2y ) ] [1+(x–2y ) ] =(1–x+2y ) (1+x–2y ) (x+2a ) 2 –4 x 2 =[(x+2a ) –2x ] [(x+2a ) +2x ] =(x+2a–2x ) (x+2a+2x ) =(2a–x ) (2a+3x ) (a+b ) 2 – (c+d ) 2 =[(a+b ) +(c+d ) ] [(a+b ) –(c+d ) ] =(a+b+c+d ) (a+b–c–d ) (a–b ) 2 – (c–d ) 2 =[(a–b ) +(c–d ) ] [(a–b ) –(c–d ) ] =(a–b+c–d ) (a–b–c+d ) (x+1 ) 2 –16 x 2 =[(x+1 ) –4x ] [(x+1 ) +4x ] =(x+1–4x ) (x+1+4x ) =(1–3x ) (5x+1 ) 64 m 2 – (m–2n ) 2 =[8m–(m–2n ) ] [8m+(m–2n ) ] =(8m–m+2n ) (8m+m–2n ) =(7m+2n ) (9m–2n ) (a–2b ) 2 – (x+y ) 2 =[(a–2b ) –(x+y ) ] [(a–2b ) +(x+y ) ] =(a–2b–x–y ) (a–2b+x+y ) (2a–c ) 2 – (a+c ) 2 =[(2a–c ) +(a+c ) ] [(2a–c ) –(a+c ) ] =(2a– c +a+ c ) (2a–c–a–c ) =3a(a–2c ) (x+1 ) 2 –4 x 2 =[(x+1 ) –2x ] [(x+1 ) +2x ] =(x+1–2x ) (x+1+2x ) =(1–x ) (3x+1 ) 36 x 2 – (a+3x ) 2 =[6x–(a+3x ) ] [6x+(a+3x ) ] =(6x–a–3x ) (6x+a+3x ) =(3x–a ) (9x+a ) a 6 – (a–1 ) 2 =[ a 3 –(a–1 ) ] [ a 3 +(a–1 ) ] =( a 3 –a+1 ) ( a 3 +a–1 ) (a–1 ) 2 – (m–2 ) 2 =[(a–1 ) –(m–2 ) ] [(a–1 ) +(m–2 ) ] =(a–1–m+2 ) (a–1+m–2 ) =(a–m+1 ) (a+m–3 ) (2x–3 ) 2 – (x–5 ) 2 =[(2x–3 ) +(x–5 ) ] [(2x–3 ) –(x–5 ) ] =(2x–3+x–5 ) (2x–3–x+5 ) =(3x–8 ) (x+2 ) 1– (5a+2x ) 2 =[1+(5a+2x ) ] [1–(5a+2x ) ] =(1+5a+2x ) (1–5a–2x ) (7x+y ) 2 –81 =[(7x+y ) –9 ] [(7x+y ) +9 ] =(7x+y–9 ) (7x+y+9 ) m 6 – ( m 2 –1 ) 2 =[ m 3 –( m 2 –1 ) ] [ m 3 +( m 2 –1 ) ] =( m 3 – m 2 +1 ) ( m 3 + m 2 –1 ) 16 a 10 – (2 a 2 +3 ) 2 =[4 a 5 –(2 a 2 +3 ) ] [4 a 5 +(2 a 2 +3 ) ] =(4 a 5 –2 a 2 –3 ) (4 a 5 +2 a 2 +3 ) (x–y ) 2 – (c+d ) 2 =[(x–y ) –(c+d ) ] [(x–y ) +(c+d ) ] =(x–y–c–d ) (x–y+c+d ) (2a+b–c ) 2 – (a+b ) 2 =[(2a+b–c ) –(a+b ) ] [(2a+b–c ) +(a+b ) ] =(2a+ b –c–a– b ) (2a+b–c+a+b ) =(a–c ) (3a+2b–c ) 100– (x–y+z ) 2 =[10–(x–y+z ) ] [10+(x–y+z ) ] =(10–x+y–z ) (10+x–y+z ) x 2 – (y–x ) 2 =[x–(y–x ) ] [x+(y–x ) ] =(x–y+x ) ( x +y– x ) =y(2x–y ) (2x+3 ) 2 – (5x–1 ) 2 =[(2x+3 ) –(5x–1 ) ] [(2x+3 ) +(5x–1 ) ] =(2x+3–5x+1 ) (2x+3+5x–1 ) =(4–3x ) (7x+2 ) (x–y+z ) 2 – (y–z+2x ) 2 =[(x–y+z ) –(y–z+2x ) ] [(x–y+z ) +(y–z+2x ) ] =(x–y+z–y+z–2x ) (x–y+z+y–z+2x ) =(x–y+z–y+z–2x ) (x– y + z + y – z +2x ) =3x(2z–2y–x ) (2x+1 ) 2 – (x+4 ) 2 =[(2x+1 ) –(x+4 ) ] [(2x+1 ) +(x+4 ) ] =(2x+1–x–4 ) (2x+1+x+4 ) =(x–3 ) (3x+5 ) (a+2x+1 ) 2 – (x+a–1 ) 2 =[(a+2x+1 ) –(x+a–1 ) ] [(a+2x+1 ) +(x+a–1 ) ] =( a +2x+1–x– a +1 ) (a+2x+ 1 +x+a– 1 ) =(x+2 ) (2a+3x ) 4 (x+a ) 2 –49 y 2 =[2(x+a ) –7y ] [2(x+a ) +7y ] =(2x+2a–7y ) (2x+2a+7y ) 25 (x–y ) 2 –4 (x+y ) 2 =[5(x–y ) –2(x+y ) ] [5(x–y ) +2(x+y ) ] =(5x–5y–2x–2y ) (5x–5y+2x+2y ) =(3x–7y ) (7x–3y ) 36 (m+n ) 2 –121 (m–n ) 2 =[6(m+n ) –11(m–n ) ] [6(m+n ) +11(m–n ) ] =(6m+6n–11m+11n ) (6m+6n+11m–11n ) =(17n–5m ) (17m–5n ) Categories: Capítulo X