$48^2+53^2+62^2=$ ?

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Answer 1 · 2015-12-25T00:16:35

$8957$

Use $(a+-b)^2 = a^2+-2ab+b^2$

$48^2 = (50-2)^2 = 50^2-2(50)(2)+2^2$

$= 2500-200+4 = color(blue)(2304)$

$53^2 = (50+3)^2 = 50^2+2(50)(3)+3^2$

$=2500+300+9 = color(blue)(2809)$

$62^2 = (50+12)^2 = 50^2+2(50)(12)+12^2$

$=2500+1200+144 = color(blue)(3844)$

So:

$48^2+53^2+62^2 = 2304+2809+3844 = 8957$

48^2+53^2+62^2=48^2+53^2+62^2=?