Question

R= (x+ 2) (x- 2) - (x+ 8) (x- 8)

Answer 1

R= (x+ 2) (x- 2) - (x+ 8) (x- 8)= 60

$\mathrm{Expandir}\:\left(x+2\right)\left(x-2\right):\quad x^2-4\\\\\left(x+2\right)\left(x-2\right)\\\\\mathrm{Aplicar\:la\:siguiente\:regla\:para\:binomios\:al\:cuadrado:\:}\left(a+b\right)\left(a-b\right)=a^2-b^2\\\\a=x,\:b=2\\\\=x^2-2^2\\\\2^2=4\\\\=x^2-4\\\\=x^2-4-\left(x+8\right)\left(x-8\right)\\\\\\\\\\\mathrm{Expandir}\:-\left(x+8\right)\left(x-8\right):\quad -x^2+64\\\\=-\left(x^2-64\right)\\\\\mathrm{Poner\:los\:parentesis}\\\\=-\left(x^2\right)-\left(-64\right)$$Aplicar\:las\:reglas\:de\:los\:signos\\\\-\left(-a\right)=a,\:\:\:-\left(a\right)=-a\\\\=-x^2+64\\\\=x^2-4-x^2+64\\\\\\\\\\\mathrm{Simplificar}\:x^2-4-x^2+64\\\\x^2-4-x^2+64\\\\\mathrm{Agrupar\:terminos\:semejantes}\\\\=x^2-x^2-4+64\\\\\mathrm{Sumar\:elementos\:similares:}\:x^2-x^2=0\\\\=-4+64\\\\\mathrm{Sumar/restar\:lo\:siguiente:}\:-4+64=60\\\\=60$