765. Разложите на множители:
a) (x + y) ^ 2 - (x - y) ^ 2
б) (2m - n) ^ 2 - (m + 2n) ^ 2
B) (3n + 2p) ^ 2 - (5p - 2n) ^ 2 ;
r) 4 * (3x - 2y) ^ 2 - 9 * (4x + 3y) ^ 2 ;
х) 100 * (6a + 3b) ^ 2 - 81 * (3a + 2b) ^ 2 ;
e) 49 * (5x ^ 2 + 8) ^ 2 - 36 * (4x ^ 2 - 1) ^ 2 .
a) (x + y) ^ 2 - (x - y) ^ 2
б) (2m - n) ^ 2 - (m + 2n) ^ 2
B) (3n + 2p) ^ 2 - (5p - 2n) ^ 2 ;
r) 4 * (3x - 2y) ^ 2 - 9 * (4x + 3y) ^ 2 ;
х) 100 * (6a + 3b) ^ 2 - 81 * (3a + 2b) ^ 2 ;
e) 49 * (5x ^ 2 + 8) ^ 2 - 36 * (4x ^ 2 - 1) ^ 2 .
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Ответ:
(x + y)2 – (x – y)2 = (x + y – x + y)(x + y + x – y) = 2y ∙ 2x = 4xy.
(2m – n)2 – (m + 2n)2 = (2m – n – m – 2n)(2m – n + m + 2n) = (m – 3n)(3m + n).
(3n + 2p)2 – (5p – 2n)2 = (3n + 2p – 5p + 2n)(3n + 2p + 5p – 2n) = (5n – 3p)(n + 7p).
4(3x – 2y)2 – 9(4x + 3y)2 = (2(3x – 2y) – 3(4x + 3y))(2(3x – 2y) + 3(4x + 3y)) = (6x – 4y – 12x – 9y)( 6x – 4y + 12x + 9y) = (– 6x – 13y)(18x + 5y) = – (6x + 13y)(18x + 5y).
100(6a + 3b)2 – 81(3a + 2b)2 = (10(6a + 3b) – 9(3a + 2b))(10(6a + 3b) + 9(3a + 2b)) = (60a + 30b – 18a – 18b)(60a + 30b + 18a + 18b) = 108(7a + 2b)(5a + 2b).
9(5x2 + 8)2 – 36(4x2 – 1)2 = (3(5x2 + 8) – 6(4x2 – 1))(3(5x2 + 8) + 6(4x2 – 1)) = (15x2 + 24 – 24x2 +6)(15x2 + 24 + 24x2 – 6) = (30 – 9х2)(39x2 + 15) = 9(10 – 3х2)(13x2 + 5).