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.

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