Question

Simplify: $(x+y{)}^2+(x-y{)}^2$;

Answer 1

Using the given identities

$(x-y{)}^2$ = $x^2-2xy+y^2$ ..... $\left(eq1\right)$
and $(x+y{)}^2$ = $x^2+2xy+y^2$ .......$\left(eq2\right)$
Using (eq 1) and (eq 2) to Simplify:-
$(x+y{)}^2$+$(x-y{)}^2$
$=$ $x^2-2xy+y^2$+ $x^2+2xy+y^2$
$=$ $x^2+x^2+y^2+y^2$
$=$ $2x^2+2y^2$

Further Simplifying we get: $2(x+y{)}^2$
Hence the answer is $2(x+y{)}^2$