Question

A partir de los binomios A=x+3, B=x-2,C=x+2,D=x+1,E=x-3 y F=x-1, halla:
a.AE-BC
b.B^2-C^2
c.BD-CF
d.DF-BC
e.CE-AB
f.(D+E)(A+F)    Lo necesito urgente.

Answer 1

$A=x+3, B=x-2,C=x+2,D=x+1,E=x-3 y F=x-1 \\ a.AE-BC \\ (x+3)(x-3)-(x-2)(x+2)=x^2-9-(x^2-4) \\=-9-4=-13 \\ b.B^2-C^2 \\ (x-2)^2-(x+2)^2\\=x^2-4x+4-(x^2+4x+4)=x^2-4x+4-x^2-4x-4 \\ =-8x \\ c.BD-CF \\ (x-2)(x+1)-(x+2)(x-1) \\ =x^2+x-2x-2-(x^2-x+2x-2) \\=x^2-x-2-(x^2+x-2) =x^2-x-2-x^2-x+2 \\=-2x \\ d.DF-BC \\ (x+1)(x-1)-(x-2)(x+2) =x^2-1-(x^2-4)\\=x^2-1-x^2+4 =3\\ e.CE-AB \\ (x+2)(x-3)-(x+3)(x-2) \\ =x^2-3x+2x-6-(x^2-2x+3x-6) \\=x^2-3x+2x-6-x^2+2x-3x+6 \\ =-2x$
$f.(D+E)(A+F) \\ (x+1+x-3)(x+3+x-1)=(2x-2)(2x+2) \\ =4x^2-4$