Question

Преобразуйте выражение в многочлен: (3x-5a)*(5a-3x); (3x-5a)^2; (3x-5a)^3; (3x-5y+2)^2; (3x-5y)*(9x^2+15xy+25y^2)

Answer 1

(3x-5a)*(5a-3x) = 15ax - 25a^2 - 9x^2 + 15ax = -25a^2 + 30ax - 9x^2
(3x - 5a)^2 = 9x^2 - 30ax + 25a^2
(3x-5a)^3 = 27x^3 - 3*9x^2*5a + 3*3x*25a^2 - 125a^3 =
= 27x^3 - 135x^2*a + 225x*a^2 - 125a^3
(3x-5y+2)^2 = 9x^2 - 30xy + 25y^2 + 12x - 20y + 4
(3x-5y)*(9x^2+15xy+25y^2) = 27x^3-45x^2*y+45x^2*y-75xy^2+75xy^2-125y^3 =
= 27x^3 - 125y^3

Answer 2

1) (3x-5a)*(5a-3x) = 15ax - 9x^2 - 25a + 15a^2

2) (3x-5a)^2 = (3x-5a)*(3x-5a) = 9x^2 - 15ax - 15ax + 25a^2 = 9x^2 - 30ax + 25a^2

3) (3x-5a)^3 = (3x-5a)*(3x-5a)*(3x-5a) = (9x^2 - 15ax - 15ax + 25a^2)*(3x-5a) = 27x^3 - 45ax^2 - 45ax^2 + 75a^2x - 27ax^2 + 45a^2x + 45a^2x - 75a^3 = 27x^3 - 81ax^2 + 120a^2x - 125a^3

4) (3x-5y+2)^2 = (3x-5y+2)*(3x-5y+2) = 9x^2 - 15xy + 6x - 15xy + 25y^2 - 10y + 6x - 10y + 4 = 9x^2 - 30xy + 12x - 20y + 29

5) (3x-5y)*(9x^2+15xy+25y^2) = 27x^3 - 45xy^2 - 45x^2y + 75xy^2 + 75x^2y + 125y^3 = 27x^3 + 30x^2y + 30xy^2 + 125y^3