Задание 1
1. a(x+y) = ax + ay
2. -p(a-b) = -pa - p*(-b) = -pa + pb = pb - pa
3. 3x²(x³-2) = 3x^5 - 3*2x^2 = 3x^5 - 6x^2
4. (2x - x^3)(-5x^4) = -2*5x^5 - (-5)x^7 = -10x^5 + 5x^7 = 5x^7 - 10x^5
5. 3x(x-2) - 5x(x+3) = 3x^2 - 6x - 5x^2 -15x = -2x^2 -21x
6. 5n^2(3n-1) - 2n(5n^2-3) = 15n^3 - 5n^2 - 10n^3 + 6n = 5n^3 - 5n^2 + 6n
Задание 2
а) 5(a+2) + (a-2) = 5a + 10 + a - 2= 6a + 8
б) 2x(x+1) - 4x(2-x) = 2x^2 + 2x - 8x + 4x^2 = 6x^2 - 6x
в) x(x^2+x) - (x^2+x+1) = x^3 + x^2 -x^2 - x - 1 = x^3 - x - 1
г) 2y^2(6y-1) + 3y(y-4y^2) = 12y^3 - 2y^2 + 3y^2 - 12y^3 = y^2
Задание 3
(a^4 - a^3b + a^2 b^2 - ab^3) a^2 b = a^6 b - a^5b^2 + a^4 b^3 - a^3 b^4
Задание 4
x = -1/3
-3x^2 + 5x + 3 = -3 * (-1/3)*(-1/3) + 5*(-1/3) + 3 = -3/9 - 5/3 +3 = -1/3 - 5/3 +3 = =-6/3 + 3 = -2 +3 = 1
Задание 5
а) n^2 - 3n + n^3 - 4n^2 + 3n - 2 = n^3 + (n^2 - 4n^2) + (3n - 3n) -2 =
= n^3 - 3n^2 -2
б) 2x^2 * 7xy^2 - 4xy^2 (-xy) - 3x*5x^2y^2 = 14x^3 y^2 + 4 x^2 y^3 -
- 15 x^3 y^2 = 4 x^2 y^3 + (14 x^3 y^2 - 15 x^3 y^2) = 4 x^2 y^3 - x^3 y^2