Question

Преобразуйте в многочлен : 1) (-a+2)^2 2) (-b-3)^2 3) (-n+4)^2 4) (-x-10)^2 5) (-2x-3y)^2 6) (-1/3a+1/2b)^2 7) (-1 целая 3х-6)^2 8) (-c+b/4)^2

Answer 1

1) =(2-a)²=4-4a+a²
2) =(-(b+3))² =(b+3)²=b²+6b+9
3) =(4-n)²=16-8n+n²
4) =(-(x+10))² =(x+10)² =x²+20x+100
5) =(-(2x+3y))² =(2x+3y)² =4x² +12xy+9y²
6) =(1/2b -1/3a)² =1/4 b² - 1/3 ab + 1/9 a²
7) = (-(1.3x+6))² =(1.3x+6)² = 1.69x²+15.6x+36
8) = (b/4 -c)² = b²/16 - 1/2 bc +c²

Answer 2

Давайте преобразуем каждое выражение в многочлен:

1. (-a+2)^2 = (-a+2)(-a+2) = (-a)(-a) + (-a)(2) + (2)(-a) + (2)(2) = a^2 - 2a - 2a + 4 = a^2 - 4a + 4

2. (-b-3)^2 = (-b-3)(-b-3) = (-b)(-b) + (-b)(-3) + (-3)(-b) + (-3)(-3) = b^2 + 3b + 3b + 9 = b^2 + 6b + 9

3. (-n+4)^2 = (-n+4)(-n+4) = (-n)(-n) + (-n)(4) + (4)(-n) + (4)(4) = n^2 - 4n - 4n + 16 = n^2 - 8n + 16

4. (-x-10)^2 = (-x-10)(-x-10) = (-x)(-x) + (-x)(-10) + (-10)(-x) + (-10)(-10) = x^2 + 10x + 10x + 100 = x^2 + 20x + 100

5. (-2x-3y)^2 = (-2x-3y)(-2x-3y) = (-2x)(-2x) + (-2x)(-3y) + (-3y)(-2x) + (-3y)(-3y) = 4x^2 + 6xy + 6xy + 9y^2 = 4x^2 + 12xy + 9y^2

6. (-1/3a+1/2b)^2 = (-1/3a+1/2b)(-1/3a+1/2b) = (-1/3a)(-1/3a) + (-1/3a)(1/2b) + (1/2b)(-1/3a) + (1/2b)(1/2b) = 1/9a^2 - 1/6ab - 1/6ab + 1/4b^2 = 1/9a^2 - 1/3ab + 1/4b^2

7. (-1 целая 3х-6)^2 = (-1 целая 3х-6)(-1 целая 3х-6) = (-1 целая 3х)(-1 целая 3х) + (-1 целая 3х)(-6) + (-6)(-1 целая 3х) + (-6)(-6) = 1 целая 9х^2 + 6 целых 3х + 6 целых 3х + 36 = 1 целая 9х^2 + 12 целых 3х + 36

8. (-c+b/4)^2 = (-c+b/4)(-c+b/4) = (-c)(-c) + (-c)(b/4) + (b/4)(