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

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Answer 1 · 2018-04-22T11:38:05

$2 x^{2} + 10 x + 13$ $2x^2+10x+13$

Expand the first two brackets:

${(x + 2)}^{2} = (x + 2) (x + 2) \to x^{2} + 4 x + 4$ $(x+2)^2=(x+2)(x+2) -> x^2+4x+4$

Expand the next two brackets:

${(x + 3)}^{2} = (x + 3) (x + 3) \to x^{2} + 6 x + 9$ $(x+3)^2=(x+3)(x+3) -> x^2+6x+9$

Collecting-like terms:

$x^{2} + 4 x + 4 + x^{2} + 6 x + 9$ $color(red)(x^2)color(blue)(+4x)color(green)(+4)color(red)(+x^2)color(blue)(+6x)color(green)(+9)$

$\to 2 x^{2} + 10 x + 13$ $-> color(red)(2x^2)+color(blue)(10x)+color(green)(13)$

$\to 2 x^{2} + 10 x + 13$ $-> 2x^2+10x+13$

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