04.19. Упростите выражение: a) xy-yxy-xx² - y² x y xy 6) 12 + 4P + P²; +3q2 q B) 3mn + 2n2m+2n m-2n; mn m n 2562 10b г) +2. 2a2 a

a) $$\frac{xy}{x} - \frac{xy}{y} - \frac{x^2 - y^2}{xy} = \frac{xy \cdot y - xy \cdot x - (x^2 - y^2)}{xy} = \frac{xy^2 - x^2y - x^2 + y^2}{xy} =$$ $$\frac{xy^2 - x^2y - x^2 + y^2}{xy}$$ б) $$12 + \frac{4p}{q} + \frac{p^2}{3q^2} = \frac{12 \cdot 3q^2 + 4p \cdot 3q + p^2}{3q^2} = \frac{36q^2 + 12pq + p^2}{3q^2}$$ в) $$\frac{3mn + 2n^2}{mn} + \frac{m + 2n}{m} + \frac{m - 2n}{n} = \frac{(3mn + 2n^2) \cdot 1 + (m + 2n) \cdot n + (m - 2n) \cdot m}{mn} = $$ $$\frac{3mn + 2n^2 + mn + 2n^2 + m^2 - 2mn}{mn} = \frac{2mn + 4n^2 + m^2}{mn} = \frac{m^2 + 2mn + 4n^2}{mn}$$ г) $$\frac{25b^2}{2a^2} - \frac{10b}{a} + 2 = \frac{25b^2}{2a^2} - \frac{10b \cdot 2a}{2a^2} + \frac{2 \cdot 2a^2}{2a^2} = \frac{25b^2 - 20ab + 4a^2}{2a^2}$$ Ответ: а) $$\frac{xy^2 - x^2y - x^2 + y^2}{xy}$$; б) $$\frac{36q^2 + 12pq + p^2}{3q^2}$$; в) $$\frac{m^2 + 2mn + 4n^2}{mn}$$; г) $$\frac{25b^2 - 20ab + 4a^2}{2a^2}$$