Упростите выражение:
а) $(2x - 3y)^2 + (2x + 3y)^2$;
б) $(2x + 3y)^2 - (2x - 3y)^2$;
в) $2(\frac{x}{2} + \frac{y}{4})^2 + (2x - y)^2$;
г) $3(\frac{x}{3} + \frac{y}{9})^2 - (3x - y)^2$.
$(2x - 3y)^2 + (2x + 3y)^2 = 4x^2 - 12xy + 9y^2 + 4x^2 + 12xy + 9y^2 = 8x^2 + 18y^2 = 2(4x^2 + 9y^2)$
$(2x + 3y)^2 - (2x - 3y)^2 = (2x + 3y - 2x + 3y)(2x + 3y + 2x - 3y) = 6y * 4x = 24xy$
$2(\frac{x}{2} + \frac{y}{4})^2 + (2x - y)^2 = 2(\frac{x^2}{4} + \frac{xy}{4} + \frac{y^2}{16}) + (4x^2 - 4xy + y^2) = \frac{x^2}{2} + \frac{xy}{2} + \frac{y^2}{8} + 4x^2 - 4xy + y^2 = 4\frac{1}{2}x^2 - 3\frac{1}{2}xy + 1\frac{1}{8}y^2$
$3(\frac{x}{3} + \frac{y}{9})^2 - (3x - y)^2 = 3(\frac{x^2}{9} + \frac{2xy}{27} + \frac{y^2}{81}) - (9x^2 - 6xy + y^2) = \frac{x^2}{3} + \frac{2xy}{9} + \frac{y^2}{27} - 9x^2 + 6xy - y^2 = -8\frac{2}{3}x^2 + 6\frac{2}{9}xy - \frac{26}{27}y^2$
Пожауйста, оцените решение
