Question

Умножение одночлена на многочлен 3a(a^2-5a+1) (4a^3+3a^2-6)*(-2a^2) 2ab*(3a^2b^2-2ab^3+5) 10xy^3(5x^4y-2x^3y^2-x^2) 8ab^4(-2a^2b+3ab^4-5a^2) 4(x-7)+5(x+6) 9(3x+1)-4(2x-7) -3b(5a-b)+6a(3b-a) -3y(2x-5y)-2y(5x-4y) 10x^3(4x+5)-8x(2x^3-x^2)

Answer 1

Ответ:

Пошаговое объяснение:

1) 3a(a² - 5a + 1) = 3a³ - 15a² + 3a;

2) (4a³ + 3a² - 6) · ( - 2a²) = - 8a⁵ - 6a⁴ + 12a²;

3) 2ab · (3a²b² - 2ab³ + 5) = 6a³b³ - 4a²b⁴ + 10ab;

4) 10xy³ · (5x⁴y - 2x³y² - x²) = 50x⁵y⁴ - 20x⁴y⁵ - 10x³y³;

5) 8ab⁴ · ( - 2a²b + 3ab⁴ - 5a²) = - 16a³b⁵ + 24a²b⁸ - 40a³b⁴;

6) 4 · (x - 7) + 5 · (x + 6) = 4x - 28 + 5x + 30 = 9x + 2;

7) 9 · (3x + 1) - 4 · (2x - 7) = 27x + 9 - 8x + 28 = 19x + 37;

8) -3b · (5a - b) + 6a · (3b - a) = - 15ab + 3b² + 6ab - 6a² =3b² - 9ab - 6a²;

9) - 3y · (2x - 5y) - 2y · (5x - 4y) = - 6xy + 15y² - 10xy + 8y² = 23y² - 16xy;

10) 10x³ · (4x + 5) - 8x · (2x³ - x²) = 40x⁴ + 50x³ - 16x⁴ + 8x³ = 24x⁴ + 58x³

Answer 2

To perform the multiplication of the given expressions, follow these steps:

1. Distribute the terms of the first factor to the terms of the second factor.
2. Simplify and combine like terms, if applicable.

Let's apply these steps to each expression:

1. $3a(a^2-5a+1) \times (4a^3+3a^2-6) \times (-2a^2)$

Step 1: Distribute the terms $3a \times (4a^3+3a^2-6) \times (-2a^2) = -6a^6 - 9a^5 + 18a^3$

Step 2: Simplify The multiplication with the constant term $(-2a^2)$ results in $(-6a^6 - 9a^5 + 18a^3) \times (-2a^2) = 12a^8 + 18a^7 - 36a^5$

Final result: $12a^8 + 18a^7 - 36a^5$

2. $2ab \times (3a^2b^2-2ab^3+5)$

Step 1: Distribute the terms $2ab \times (3a^2b^2-2ab^3+5) = 6a^3b^3 - 4a^2b^4 + 10ab$

Final result: $6a^3b^3 - 4a^2b^4 + 10ab$

3. $10xy^3 \times (5x^4y-2x^3y^2-x^2)$

Step 1: Distribute the terms $10xy^3 \times (5x^4y-2x^3y^2-x^2) = 50x^5y^4 - 20x^4y^5 - 10x^3y^3$

Final result: $50x^5y^4 - 20x^4y^5 - 10x^3y^3$

4. $8ab^4 \times (-2a^2b+3ab^4-5a^2)$

Step 1: Distribute the terms $8ab^4 \times (-2a^2b+3ab^4-5a^2) = -16a^3b^5 + 24a^2b^8 - 40ab^4$

Final result: $-16a^3b^5 + 24a^2b^8 - 40ab^4$

5. $4(x-7)+5(x+6)$

Step 1: Distribute the terms $4(x-7)+5(x+6) = 4x - 28 + 5x + 30$

Step 2: Simplify $4x + 5x - 28 + 30 = 9x + 2$