Разложите на множители:
а) $2(x - y) + (x - y)^2$;
б) $(a + b)^2 - (a + b)(a - b)$;
в) $x(x - y)^2 - y(y - x)^2$;
г) (x − y) + x(y − x);
д) $n(m - n)^2 - (n - m)^3$;
е) $a(a - c)^2 - c(a - c)(c - a)$.
$2(x - y) + (x - y)^2 = (x - y)(2 + x - y)$
$(a + b)^2 - (a + b)(a - b) = (a + b)(a + b - (a - b)) = (a + b)(a + b - a + b) = 2b(a + b)$
$x(x - y)^2 - y(y - x)^2 = x(x - y)^2 - y(x - y)^2 = (x - y)^2(x - y) = (x - y)^3$
(x − y) + x(y − x) = (x − y) − x(x − y) = (x − y)(1 − x)
$n(m - n)^2 - (n - m)^3 = n(n - m)^2 - (n - m)^3 = (n - m)^2(n - (n - m)) = (n - m)^2(n - n + m) = m(n - m)^2$
$a(a - c)^2 - c(a - c)(c - a) = a(a - c)^2 + c(a - c)(a - c) = a(a - c)^2 + c(a - c)^2 = (a - c)^2(a + c)$
Пожаулйста, оцените решение
