Question

1.) Упростить выражения: 1) (х – 4)2 – 6; 2) 10а + (а – 5)2; 3) (3m – 7n)2 – 9m(n – 5n); 4) (6а – 3b)2 + (9а + 2b)2; 5) b(b – 3) – (b – 4)2; 6) (12а – b)2 – (9а – b)(16а + 2b); 7) х(2х – 9)2 – 2х(15 + х)2; 8) (х + 2)2 – (х – 3)(х + 3); 9) (7а – 5b)(7а + 5b) – (4а + 7b)2; 10) (у – 2)(у + 3) – (у – 1)2 + (5 – у)(у + 5).

Answer 1

Ответ:

1)(6-4)2х

2)(10-5)+2а

3)(5-3)-(9-7)nm

4)упрощённо не надо упрощать

5)b-b(4-3×2)b

6)упрощённо не надо упрощать

7)упрощённо не надо упрощать

Answer 2

1) (х – 4)² – 6 To simplify this expression, we need to expand the square. (х – 4)² = (х – 4) * (х – 4) = х² – 8х + 16

Substituting this back into the expression: (х – 4)² – 6 = х² – 8х + 16 – 6 = х² – 8х + 10

2) 10а + (а – 5)² Again, we need to expand the square: (а – 5)² = (а – 5) * (а – 5) = а² – 10а + 25

Substituting this back into the expression: 10а + (а – 5)² = 10а + (а² – 10а + 25) = 10а + а² – 10а + 25 = а² + 25

3) (3m – 7n)² – 9m(n – 5n) Expanding the square: (3m – 7n)² = (3m – 7n) * (3m – 7n) = 9m² – 42mn + 49n²

Substituting this back into the expression: (3m – 7n)² – 9m(n – 5n) = 9m² – 42mn + 49n² – 9m(–4n) = 9m² – 42mn + 49n² + 36mn = 9m² – 6mn + 49n²

4) (6а – 3b)² + (9а + 2b)² Expanding the squares: (6а – 3b)² = (6а – 3b) * (6а – 3b) = 36а² – 36ab + 9b² (9а + 2b)² = (9а + 2b) * (9а + 2b) = 81а² + 36ab + 4b²

Adding these two expressions together: (6а – 3b)² + (9а + 2b)² = 36а² – 36ab + 9b² + 81а² + 36ab + 4b² = 117а² + 13b²

5) b(b – 3) – (b – 4)² Expanding the square: (b – 4)² = (b – 4) * (b – 4) = b² – 8b + 16

Substituting this back into the expression: b(b – 3) – (b – 4)² = b² – 3b – b² + 8b – 16 = 5b – 16

6) (12а – b)² – (9а – b)(16а + 2b) Expanding the square: (12а – b)² = (12а – b) * (12а – b) = 144а² – 24ab + b²

Expanding the product (9а – b)(16а + 2b): (9а – b)(16а + 2b) = 144а² + 18ab - 9b²

Substituting these back into the expression: (12а – b)² – (9а – b)(16а + 2b) = 144а² – 24ab + b² - (144а² + 18ab - 9b²) = 144а² – 24ab + b² - 144а² - 18ab + 9b² = -42ab + 10b²

7) х(2х – 9)² – 2х(15 + х)² Expanding the squares: (2х – 9)² = (2х – 9) * (2х – 9) = 4х² – 36х + 81 (15 + х)² = (15 + х) * (15 + х) = х² + 30х + 225

Substituting these back into the expression: х(2х – 9)² – 2х(15 + х)² = х(4х² – 36х + 81) – 2х(х² + 30х + 225) = 4х³ – 36х² + 81х – 2х³ – 60х² – 450х = 2х³ – 96х² – 369х

8) (х + 2)² – (х – 3)(х + 3) Expanding the square: (х + 2)² = (х + 2) * (х + 2) = х² + 4х + 4

Expanding the product (х – 3)(х + 3): (х – 3)(х + 3) = х² – 9

Substituting these back into the expression: (х + 2)² – (х – 3)(х + 3) = х² + 4х + 4 – (х² – 9) = 4х + 13

9) (7а – 5b)(7а + 5b) – (4а + 7b)² Expanding the product (7а – 5b)(7а + 5b): (7а – 5b)(7а + 5b) = 49а² – 25b²

Expanding the square: (4а + 7b)² = (4а + 7b) * (4а + 7b) = 16а² + 56ab + 49b²

Substituting these back into the expression: (7а – 5b)(7а + 5b) – (4а + 7b)² = 49а² – 25b² – (16а² + 56ab + 49b²) = 49а² – 25b² – 16а² - 56ab - 49b² = 33а² - 56ab - 74b²

10) (у – 2)(у + 3) – (у – 1)² + (5 – у)(у + 5) Expanding the products: (у – 2)(у + 3) = у² + у - 6 (у – 1)² = у² - 2у + 1 (5 – у)(у + 5) = 25 - у²

Substituting these back into the expression: (у – 2)(у + 3) – (у – 1)² + (5 – у)(у + 5) = у² + у - 6 - (у² - 2у + 1) + (25 - у²) = у² + у - 6 - у² + 2у - 1 + 25 - у² = 3у - 18

So, the simplified expressions are: 1) х² – 8х + 10 2) а² + 25 3) 9m² – 6mn + 49n² 4) 117а² + 13b² 5) 5b – 16 6) -42ab + 10b² 7) 2х³ – 96х² – 369х 8) 4х + 13 9) 33а² - 56ab - 74b² 10) 3у - 18