How do you simplify #(x + 2) ^ { 2} + ( x + 3) ^ { 2}#?

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Answer 1 · 2018-04-22T11:38:05

#2x^2+10x+13#

Expand the first two brackets:

#(x+2)^2=(x+2)(x+2) -> x^2+4x+4#

Expand the next two brackets:

#(x+3)^2=(x+3)(x+3) -> x^2+6x+9#

Collecting-like terms:

#color(red)(x^2)color(blue)(+4x)color(green)(+4)color(red)(+x^2)color(blue)(+6x)color(green)(+9)#

#-> color(red)(2x^2)+color(blue)(10x)+color(green)(13)#

#-> 2x^2+10x+13#