Question

1. Спростити вираз: 1) ( 3с – m)²; 1) (4a – c)²;2) ( 4a ² + a)²; 2) (3x 4 + x)²;3) (5m – 3)(5m + 3); 3) (2a – 5)(2a + 5);4) (3b + 5 a)(5a – 3b); 4) (3c + 4 b)(4b – 3 c);5) (a – 3)(a + 3) – 2a(5a – 3); 5) (x – 3)(x + 3) – 2 x(x – 4);6) 4a (a – 2) – (a – 4)²; 6) 4a(a – 3) – (a – 6)²;7) 3(x + 1)² - 6 x. 7) 3(a – 1) ² + 6 a.2. Розв’язати рівняння:1) (х – 4)² - х(х – 7) = 16; 1) (х – 5)² - х(х – 4) = 25;2) (2х – 5)² - (2х – 3)(2х + 3) = 114. 2) (2 - 3х) ² - (3х – 5)(3х + 5) = 114.ПОМОГИТЕ СРОЧНО​

Answer 1

1) (3с-m)²=9c²-6cm+m²

1) (4a-c)²=16a²-8ac+c²

2) (4a²+a)²=(16a⁴+8a³+a²)

2) (3x⁴+x)²=9x⁸+6x⁵+x²

3) (5m-3)(5m+3) = 25m²-9

3) (2a-5)(2a+5)=4a²-45

4) (3b+5a)(5a-3b) = 25a² - 9b²

4) (3c+4b)(4b-3c) = 16b²-9c²

5) (a-3)(a+3)-2a(5a-3) = a²-9-10a²+6a=-9a²+6a-9

5) (x-3)(x+3)-2x(x-4) = x²-9-2x²+8x = -x²+8x-9

6) 4a(a-2)-(a-4)² = 4a²-8a-a²+8a-16=3a²-16

6) 4a(a-3)-(a-6)²=4a²-12a-a²+12a-36=3a²-36

7) 3(x+1)²-6x = 3x²+6x+3-6x=3x²+3

7) 3(a-1)²+6a = 3a²-6a+3+6a=3a²+3

Задание 2

1) (х-4)²-х(х-7) = 16

х²-8х+16-х²+7х = 16

х=0

1) (х-5)² - х(х-4) = 25

х²-10х+25-х²+4х = 25

-6х= 0

х=0

2) (2х-5)²-(2х-3)(2х+3) = 114

4х²-20х+25-4х²+9=114

-20х=80

х=-4

2) (2-3х)²-(3х-5)(3х+5)=114

4-12х+9х²-9х²+25=114

-12х=85

х= - 85/12

Answer 2

Розв'язання виразів:

1. (3с - m)² = 9c² - 6cm + m²

2. (4a - c)² = 16a² - 8ac + c²

3. (4a² + a)² = 16a⁴ + 8a³ + a²

4. (3x⁴ + x)² = 9x⁸ + 6x⁵ + x²

5. (5m - 3)(5m + 3) = 25m² - 9

6. (2a - 5)(2a + 5) = 4a² - 25

7. (3b + 5a)(5a - 3b) = 15ab - 9b² + 25a² - 15ab

8. (3c + 4b)(4b - 3c) = 12b² - 9c² + 16bc

9. (a - 3)(a + 3) - 2a(5a - 3) = a² - 9 - 10a² + 6a

10. (x - 3)(x + 3) - 2x(x - 4) = x² - 9 - 2x² + 8x

11. 4a(a - 2) - (a - 4)² = 4a² - 8a - (a² - 8a + 16) = 4a² - 8a - a² + 8a - 16 = 3a² - 16

12. 4a(a - 3) - (a - 6)² = 4a² - 12a - (a² - 12a + 36) = 4a² - 12a - a² + 12a - 36 = 3a² - 36

13. 3(x + 1)² - 6x = 3(x² + 2x + 1) - 6x = 3x² + 6x + 3 - 6x = 3x² + 3

14. 3(a - 1)² + 6a = 3(a² - 2a + 1) + 6a = 3a² - 6a + 3 + 6a = 3a² + 3

Розв'язання рівнянь:

1. (x - 4)² - x(x - 7) = 16 (x² - 8x + 16) - (x² - 7x) = 16 x² - 8x + 16 - x² + 7x = 16 -x + 16 = 16 -x = 0 x = 0

2. (x - 5)² - x(x - 4) = 25 (x² - 10x + 25) - (x² - 4x) = 25 x² - 10x + 25 - x² + 4x = 25 -6x + 25 = 25 -6x = 0 x = 0

3. (2x - 5)² - (2x - 3)(2x + 3) = 114 (4x² - 20x + 25) - (4x² - 9) = 114 4x² - 20x + 25 - 4x² + 9 = 114 -20x + 25 + 9 = 114 -20x + 34 = 114 -20x = 114 - 34 -20x = 80 x = -80 / 20 x = -4

4. (2 - 3x)² - (3x - 5)(3x + 5) = 114 (4 - 12x + 9x²) - (9x² - 25) = 114 4 - 12x + 9x² - 9x² + 25 = 114 -12x + 4 + 25 = 114 -12x + 29 = 114 -12x = 114 - 29 -12x = 85 x = -85 / 12 x = -7.08 (округлено до двох знаків після коми)