1. Simplify the following expressions: (ax+1-6)(ax+1-5), (x-2y+z-3r)2, 24a2xy2-36x2y4, (a+3)(a+1)-4(a+1), a2b3-n4+a2b3x2-n4x2-3a2b3x+3n4x, 1/25+25x4/36-x2/3=5x2/6- 1/5, 121x4—133x2y4+36y8, c2+24c+135, 30x2+13

1. INSTITUTO TECNOLÓGICO DE TUXTEPEC MATEMÁTICAS. MIGUEL ÁNGEL LARA CAMACHO LIC. MARÍA DE LOS ÁNGELES 1.- (ax+1-6)(ax+1-5)= a2x+2-11ax+1+30 2.- (x-2y+z-3r)2= =x2-4y2+z2-9r2+2(x)(-2y)+2(x)(z)+2(x)(-3r)+2(-2y)(z)+2(-2y) (-3r)+2(z)(-3r) =x2-4y2+z2-9r2-4xy+2xz-6xr-4yz+12yr-6zr 3.- a) 24a2xy2-36x2y4= =(12xy2)(2a2-3xy) b) (a+3)(a+1)-4(a+1)= =a2+4a+3-4(a+1) =a2-1 c)a2b3-n4+a2b3x2-n4x2-3a2b3x+3n4x= =a2b3+a2b3x2-3a2b3-n4-n4x2+3n4x =a2b3 (1+x2-3x)-n4(1+x2-3x) =(a2b3-n4)(1+x2-3x) d)1/25+25x4/36-x2/3=5x2/6- 1/5 =25x4/36-x2/3+1/25 5x2/6 1/5 e)x2/100-y2z4/81 = =(x/10-yz2/9)(x/10-yz2/9)

2. INSTITUTO TECNOLÓGICO DE TUXTEPEC MATEMÁTICAS. MIGUEL ÁNGEL LARA CAMACHO LIC. MARÍA DE LOS ÁNGELES f)121x4—133x2y4+36y8= =(11x2+6y4) (11x2+6y4)-265x2y4 g) c2+24c+135= =(c+15)(c+9) h) 30x2+13x-10= =30(30x2)+30(13x)-30(10) =900x2+30(13x)-300 =(30x+25)(30x-12)/30 =(30x+25)(30x-12)/5*6 =(6x+5)(5x-2) 4.- a) (1+3a2-3a-a3)= (-a+1)3 = -a3+3a2-3a+1 a 1 b) 27a3-b3= (27a-b)(a2+ab+b)