889. Упростите выражение: a) (x - 2)(x + 2) – x(x + 5); б) m(m - 4) + (3 - m)(3 + m); в) (4х – а)(4x + a) + 2x(x - а); г) 2а(а + b) - (2a + b)(2a - b); д) (5а – 3c)(5a + 3c) - (7c - a)(7c + a); e) (4b + 10c)(10c - 4b) + (-5c + 2b)(5c + 2b); ж) (3х – 4y)² - (3x – 4y)(3x + 4y); 3) (2а + 6b)(6b - 2a) - (2a + 6b)².

Решение:

а) \( (x - 2)(x + 2) - x(x + 5) = (x^2 - 4) - (x^2 + 5x) = x^2 - 4 - x^2 - 5x = -5x - 4 \)

б) \( m(m - 4) + (3 - m)(3 + m) = (m^2 - 4m) + (9 - m^2) = m^2 - 4m + 9 - m^2 = -4m + 9 \)

в) \( (4x - a)(4x + a) + 2x(x - a) = (16x^2 - a^2) + (2x^2 - 2ax) = 16x^2 - a^2 + 2x^2 - 2ax = 18x^2 - 2ax - a^2 \)

г) \( 2a(a + b) - (2a + b)(2a - b) = (2a^2 + 2ab) - (4a^2 - b^2) = 2a^2 + 2ab - 4a^2 + b^2 = -2a^2 + 2ab + b^2 \)

д) \( (5a - 3c)(5a + 3c) - (7c - a)(7c + a) = (25a^2 - 9c^2) - (49c^2 - a^2) = 25a^2 - 9c^2 - 49c^2 + a^2 = 26a^2 - 58c^2 \)

е) \( (4b + 10c)(10c - 4b) + (-5c + 2b)(5c + 2b) = -(10c + 4b)(10c - 4b) + (2b - 5c)(2b + 5c) = -(100c^2 - 16b^2) + (4b^2 - 25c^2) = -100c^2 + 16b^2 + 4b^2 - 25c^2 = 20b^2 - 125c^2 \)

ж) \( (3x - 4y)^2 - (3x - 4y)(3x + 4y) = (9x^2 - 24xy + 16y^2) - (9x^2 - 16y^2) = 9x^2 - 24xy + 16y^2 - 9x^2 + 16y^2 = -24xy + 32y^2 \)

з) \( (2a + 6b)(6b - 2a) - (2a + 6b)^2 = -(2a + 6b)(2a - 6b) - (2a + 6b)^2 = -(4a^2 - 36b^2) - (4a^2 + 24ab + 36b^2) = -4a^2 + 36b^2 - 4a^2 - 24ab - 36b^2 = -8a^2 - 24ab \)