Упростите выражение:
а) a(a − b) + b(a + b) + (a − b)(a + b);
б) $(m - n)(n + m) - (m - n)^2 + 2n^2$;
в) $(c - d)^2 - (c + d)(d - c) + 2cd$;
г) (2a + 5b)(5a − 2b) − 3(a + 2b)(a − 2b);
д) $(p + 6)^2 - 4(3 - p)(3 + p)$;
е) $-(2 + m)^2 + 2(1 + m)^2 - 2(1 - m)(m + 1)$;
ж) $(x + y)^2 - (x - y)^2$;
з) $(m - n)^2 - (m + n)^2$.
$a(a - b) + b(a + b) + (a - b)(a + b) = a^2 - ab + ab + b^2 + a^2 - b^2 = 2a^2$
$(m - n)(n + m) - (m - n)^2 + 2n^2 = (m - n)(m + n) - (m - n)^2 + 2n^2 = m^2 - n^2 - (m^2 - 2mn + n^2) + 2n^2 = m^2 - n^2 - m^2 + 2mn - n^2 + 2n^2 = 2mn$
$(c - d)^2 - (c + d)(d - c) + 2cd = (c - d)^2 - (d + c)(d - c) + 2cd = c^2 - 2cd + d^2 - (d^2 - c^2) + 2cd = c^2 - 2cd + d^2 - d^2 + c^2 + 2cd = 2c^2$
$(2a + 5b)(5a - 2b) - 3(a + 2b)(a - 2b) = 10a^2 + 25ab - 4ab - 10b^2 - 3(a^2 - 4b^2) = 10a^2 + 21ab - 10b^2 - 3a^2 + 12b^2 = 7a^2 + 21ab + 2b^2$
$(p + 6)^2 - 4(3 - p)(3 + p) = p^2 + 12p + 36 - 4(9 - p^2) = p^2 + 12p + 36 - 36 + 4p^2 = 5p^2 + 12p$
$-(2 + m)^2 + 2(1 + m)^2 - 2(1 - m)(m + 1) = -(2 + m)^2 + 2(1 + m)^2 - 2(1 - m)(1 + m) = -(4 + 4m + m^2) + 2(1 + 2m + m^2) - 2(1 - m^2) = -4 - 4m - m^2 + 2 + 4m + 2m^2 - 2 + 2m^2 = 3m^2 - 4$
$(x + y)^2 - (x - y)^2 = x^2 + 2xy + y^2 - (x^2 - 2xy + y^2) = x^2 + 2xy + y^2 - x^2 + 2xy - y^2 = 4xy$
$(m - n)^2 - (m + n)^2 = m^2 - 2mn + n^2 - (m^2 + 2mn + n^2) = m^2 - 2mn + n^2 - m^2 - 2mn - n^2 = -4mn$
Пожауйста, оцените решение