Question

(x+5)²-(x+3)²-(x+1)²

Answer 1

▪A tomar en cuenta:
$\boxed{{(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }$

▪Enunciado:
$\boxed{ {(x + 5)}^{2} - {(x + 3)}^{2} - {(x + 1)}^{2} }$

° Aplicamos productos notables:
${(x + 5)}^{2} - {(x + 3)}^{2} - {(x + 1)}^{2} = \\ \\ ({x}^{2} + 2(x)(5) + {5}^{2} ) - ( {x}^{2} + 2(x)(3) + {3}^{2} ) - ( {x}^{2} + 2(x)(1) + {1}^{2} ) = \\ \\ {x}^{2} + 10x + 25 - ({x}^{2} + 6x + 9 )- ({x}^{2} + 2x + 1 )=$

${x}^{2} + 10x + 25 - {x}^{2} - 6x - 9 - {x}^{2} - 2x - 1$

° Reducimos términos semejantes:
${x}^{2} + 10x + 25 - {x}^{2} - 6x - 9 - {x}^{2} - 2x - 1 = \\ \\ {x}^{2} - {x}^{2} - {x}^{2}+10x-6x-2x+25-9-1=\\\\{x}^{2} - 2{x}^{2} +10x-8x+25-10=\\\\- {x}^{2} + 2x + 15 =\\ \\ \boxed{-({x}^{2}-2x-15)}$