Question

Simplify.

(x − 2y +3)² + (x + 2y − 3)²

Answer 1

It is known that,

$${(a+b+c)}^2=a^2+b^2+c^2+2ab+2bc+2ca$$

$${(x-2y+3)}^2+{(x+2y-3)}^2$$

$$={\left(x\right)}^2+{(-2y)}^2+{\left(3\right)}^2+2\times x\times (-2y)+2\times (-2y)\times 3+2\times 3\times x+{\left(x\right)}^2+{\left(2y\right)}^2+{(-3)}^2+2\times x\times 2y+2\times \left(2y\right)\times (-3)+2\times (-3)\times x$$

$$=x^2+4y^2+9-4xy-12y+6x+x^2+4y^2+9+4xy-12y-6x$$

$$=2x^2+8y^2+18-24y$$