№46
Вопрос
Номер 1
Выполните умножение многочленов:
а) (m – n)(m + n); б) (2a – 1)(2a + 1); в) (4y + 3x)(3x – 4y); г) (9a – 5b)(5b + 9a).
а) (m – n)(m + n);
б) (2a – 1)(2a + 1);
в) (4y + 3x)(3x – 4y);
г) (9a – 5b)(5b + 9a).
а) (m – n)(m + n) = m 2 – mn + mn – n 2 = m 2 – n 2 б) (2a – 1)(2a + 1) = 4a 2 – 2a + 2a – 1 = 4a 2 – 1 в) (4y + 3x)(3x – 4y) = 12xy + 9x 2 – 16y 2 – 12xy = 9x 2 – 16y 2 г) (9a – 5b)(5b + 9a) = 40ab – 25b 2 + 81a 2 – 40ab = 81a 2 – 25b 2
а) (m – n)(m + n) = m 2 – mn + mn – n 2 = m 2 – n 2
б) (2a – 1)(2a + 1) = 4a 2 – 2a + 2a – 1 = 4a 2 – 1
в) (4y + 3x)(3x – 4y) = 12xy + 9x 2 – 16y 2 – 12xy = 9x 2 – 16y 2
г) (9a – 5b)(5b + 9a) = 40ab – 25b 2 + 81a 2 – 40ab = 81a 2 – 25b 2
Вопрос
Номер 2
Найдите значение выражения:
а) (20 – 1)(20 + 1); б) 42 ∙ 38; в) 299 ∙ 301; г) 40,1 ∙ 39,9.
а) (20 – 1)(20 + 1);
б) 42 ∙ 38;
в) 299 ∙ 301;
г) 40,1 ∙ 39,9.
а) (20 – 1)(20 + 1) = 20 2 – 1 2 = 400 – 1 = 399 б) 42 ∙ 38 = (40 + 2)(40 – 2) = 40 2 – 2 2 = 1600 – 4 = 1596 в) 299 ∙ 301 = (300 – 1)(300 + 1) = 300 2 – 1 2 = 90000 – 1 = 89999 г) 40,1 ∙ 39,9 = (40 + 0,1)(40 – 0,1) = 40 2 – 0,1 2 = 1600 – 0,01 = 1599,99
а) (20 – 1)(20 + 1) = 20 2 – 1 2 = 400 – 1 = 399
б) 42 ∙ 38 = (40 + 2)(40 – 2) = 40 2 – 2 2 = 1600 – 4 = 1596
в) 299 ∙ 301 = (300 – 1)(300 + 1) = 300 2 – 1 2 = 90000 – 1 = 89999
г) 40,1 ∙ 39,9 = (40 + 0,1)(40 – 0,1) = 40 2 – 0,1 2 = 1600 – 0,01 = 1599,99
Вопрос
Номер 3
Решите уравнение:
а) (2х – 5)(2х + 5) – 4х(х + 2) = 7; б) 4,5у(2у + 1/3 ) – 7 = (3у – 2)(3у + 2).
а) (2х – 5)(2х + 5) – 4х(х + 2) = 7;
б) 4,5у(2у + 1/3 ) – 7 = (3у – 2)(3у + 2).
1/3
а) (2х – 5)(2х + 5) – 4х(х + 2) = 7 4х 2 – 25 – 4х 2 – 8х = 7 – 25 – 8х = 7 8х = – 25 – 7 8х = – 32 х = – 4 б) 4,5у(2у + 1/3 ) – 7 = (3у – 2)(3у + 2) 9у 2 + 1,5у – 7 = 9у 2 – 4 1,5у – 7 = – 4 1,5у = 7 – 4 1,5у = 3 у = 2
а) (2х – 5)(2х + 5) – 4х(х + 2) = 7
4х 2 – 25 – 4х 2 – 8х = 7
– 25 – 8х = 7
8х = – 25 – 7
8х = – 32
х = – 4
б) 4,5у(2у + 1/3 ) – 7 = (3у – 2)(3у + 2)
1/3
9у 2 + 1,5у – 7 = 9у 2 – 4
1,5у – 7 = – 4
1,5у = 7 – 4
1,5у = 3
у = 2
Вопрос
Номер 1
Выполните умножение многочленов:
а) (k – p)(k + p); б) (3b – 1)(3b + 1); в) (5x + 3y)(3y – 5x); г) (8m – 7n)(7n + 8m).
а) (k – p)(k + p);
б) (3b – 1)(3b + 1);
в) (5x + 3y)(3y – 5x);
г) (8m – 7n)(7n + 8m).
а) (k – p)(k + p) = k 2 – kp + kp – p 2 = k 2 – p 2 б) (3b – 1)(3b + 1) = 9b 2 – 3b + 3b – 1 = 9b 2 – 1 в) (5x + 3y)(3y – 5x) = 15xy + 9y 2 – 25x 2 – 15xy = 9y 2 – 25x 2 г) (8m – 7n)(7n + 8m) = 56mn – 49n 2 + 64m 2 – 56mn = 64m 2 – 49n 2
а) (k – p)(k + p) = k 2 – kp + kp – p 2 = k 2 – p 2
б) (3b – 1)(3b + 1) = 9b 2 – 3b + 3b – 1 = 9b 2 – 1
в) (5x + 3y)(3y – 5x) = 15xy + 9y 2 – 25x 2 – 15xy = 9y 2 – 25x 2
г) (8m – 7n)(7n + 8m) = 56mn – 49n 2 + 64m 2 – 56mn = 64m 2 – 49n 2
Вопрос
Номер 2
Найдите значение выражения:
а) (30 – 1)(30 + 1); б) 62 ∙ 58; в) 499 ∙ 501; г) 20,1 ∙ 19,9.
а) (30 – 1)(30 + 1);
б) 62 ∙ 58;
в) 499 ∙ 501;
г) 20,1 ∙ 19,9.
а) (30 – 1)(30 + 1) = 30 2 – 1 2 = 900 – 1 = 899 б) 62 ∙ 58 = (60 + 2)(60 – 2) = 60 2 – 2 2 = 3600 – 4 = 3596 в) 499 ∙ 501 = (500 – 1)(500 + 1) = 500 2 – 1 2 = 250000 – 1 = 249999 г) 20,1 ∙ 19,9 = (20 + 0,1)(20 – 0,1) = 20 2 – 0,1 2 = 400 – 0,01 = 399,99
а) (30 – 1)(30 + 1) = 30 2 – 1 2 = 900 – 1 = 899
б) 62 ∙ 58 = (60 + 2)(60 – 2) = 60 2 – 2 2 = 3600 – 4 = 3596
в) 499 ∙ 501 = (500 – 1)(500 + 1) = 500 2 – 1 2 = 250000 – 1 = 249999
г) 20,1 ∙ 19,9 = (20 + 0,1)(20 – 0,1) = 20 2 – 0,1 2 = 400 – 0,01 = 399,99
Вопрос
Номер 3
Решите уравнение:
а) (3х – 4)(3х + 4) – 9х(х + 2) = 20; б) 12,5у(2у + 1/5 ) – 11 = (5у – 6)(5у + 6).
а) (3х – 4)(3х + 4) – 9х(х + 2) = 20;
б) 12,5у(2у + 1/5 ) – 11 = (5у – 6)(5у + 6).
1/5
а) (3х – 4)(3х + 4) – 9х(х + 2) = 20 9х 2 – 16 – 9х 2 – 18х = 20 – 16 – 18х = 20 18х = – 16 – 20 18х = – 36 х = – 2 б) 12,5у(2у + 1/5 ) – 11 = (5у – 6)(5у + 6) 25у 2 + 2,5у – 11 = 25у 2 – 36 2,5у = 11 – 36 2,5у = – 25 у = – 10
а) (3х – 4)(3х + 4) – 9х(х + 2) = 20
9х 2 – 16 – 9х 2 – 18х = 20
– 16 – 18х = 20
18х = – 16 – 20
18х = – 36
х = – 2
б) 12,5у(2у + 1/5 ) – 11 = (5у – 6)(5у + 6)
1/5
25у 2 + 2,5у – 11 = 25у 2 – 36
2,5у = 11 – 36
2,5у = – 25
у = – 10
