Question

1) а(3а2+а) = 2) (6к2-а)(-2к) = 3) -5р2(2р4-3) = 4) в(2в3-7) = 5) 4m3(n-5m) = 6) (в-2ас) * 5ав = 7) -р2(3q-2p) = 8) -2у2(у3-1) = 9) х5(-х3-х2) = 10) 3n2(4n-6m) = 11) а(а+в) -в(а-в) = 12) 5а+2а(3а-2) = 13) 2х(х-у) - у(у-2х) = 14) 2ху+2х(х-у) = 15) а(а2-1) +а2(а-1) =

Answer 1

Решение
1) а(3а²+а) = 3a³ + a²2) (6к²-а)(-2к) = - 12k³+ 2ak
3) -5р²(2р⁴-3) = - 10p⁶ + 15p²
4) в(2в³-7) = 2b⁴ - 7b
5) 4m³(n-5m) = 4m³n - 20m⁴
6) (в-2ас) * 5ав = 5ab² - 10a²bc
7) -р²(3q-2p) = - 3p²q + 2p³
8) -2у²(у³-1) =- 2y⁵+ 2y²
9) х⁵(-х³-х²) = - x⁸ - x⁷
10) 3n²(4n-6m) = 12n³ - 18mn²
11) а(а+в) -в(а-в) = a² + ab - ab + b² = a² + b²
12) 5а+2а(3а-2) = 5a + 6a² - 4a = 6a² + a
13) 2х(х-у) - у(у-2х) = 2x² - 2xy - y² + 2xy = 2x² - y²
14) 2ху+2х(х-у) = 2xy + 2x² - 2xy = 2x²
15) а(а²-1) +а²(а-1) = a³ - a + a³ - a² = 2a³ - a² - a

Answer 2

Давайте решим систему уравнений:

1) \(a(3a^2 + a) = 2\)

Решение: \(a(3a^2 + a) = 3a^3 + a^2 = 2\) \(3a^3 + a^2 - 2 = 0\)

2) \((6k^2 - a)(-2k) = -3\)

Решение: \((-2k)(6k^2 - a) = -12k^3 + 2ak = -3\) \(12k^3 - 2ak = 3\)

3) \(-5p^2(2p^4 - 3) = 0\)

Решение: \(-5p^2(2p^4 - 3) = -10p^6 + 15p^2 = 0\) \(p^2(15 - 10p^4) = 0\) \(p^2 = 0\) или \(15 - 10p^4 = 0\) \(p = 0\) или \(p^4 = \frac{15}{10} = \frac{3}{2}\)

4) \(b(2b^3 - 7) = 0\)

Решение: \(b(2b^3 - 7) = 2b^4 - 7b = 0\) \(b(2b^3 - 7) = b(2b^3 - 7) = 0\) \(b = 0\) или \(2b^3 - 7 = 0\) \(2b^3 = 7\) \(b^3 = \frac{7}{2}\)

5) \(4m^3(n - 5m) = 0\)

Решение: \(4m^3(n - 5m) = 4m^3n - 20m^4 = 0\) \(m^3(4n - 20m) = 0\) \(m^3 = 0\) или \(4n - 20m = 0\) \(m = 0\) или \(4n = 20m\) \(n = 5m\)

6) \((b - 2ac) \times 5ab = 0\)

Решение: \((b - 2ac) \times 5ab = 5ab(b - 2ac) = 0\) \(b - 2ac = 0\) или \(ab = 0\)

7) \(-p^2(3q - 2p) = 0\)

Решение: \(-p^2(3q - 2p) = -3p^3q + 2p^3 = 0\) \(p^3(2 - 3q) = 0\) \(p = 0\) или \(3q = 2\)

8) \(-2y^2(y^3 - 1) = 0\)

Решение: \(-2y^2(y^3 - 1) = -2y^5 + 2y^2 = 0\) \(y^2(-2y^3 + 2) = 0\) \(y^2 = 0\) или \(-2y^3 + 2 = 0\) \(y = 0\) или \(2 = 2y^3\) \(y^3 = 1\) \(y = 1\)

9) \(x^5(-x^3 - x^2) = 0\)

Решение: \(x^5(-x^3 - x^2) = -x^8 - x^7 = 0\) \(x^7(x + 1) = 0\) \(x = 0\) или \(x = -1\)

10) \(3n^2(4n - 6m) = 0\)

Решение: \(3n^2(4n - 6m) = 12n^3 - 18mn^2 = 0\) \(n^2(4n - 6m) = 0\) \(n^2 = 0\) или \(4n - 6m = 0\) \(n = 0\) или \(4n = 6m\) \(n = \frac{3}{2}m\)

11) \(a(a + b) - b(a - b) = 0\)

Решение: \(a(a + b) - b(a - b) = a^2 + ab - a^2 + ab = 2ab = 0\) \(ab = 0\)

12) \(5a + 2a(3a - 2) = 0\)

Решение: \(5a + 2a(3a - 2) = 5a + 6a^2 - 4a = 6a^2 + a = 0\) \(a(6a + 1) = 0\) \(a = 0\) или \(6a + 1 = 0\) \(a = 0\) или \(6a = -1\) \(a = -\frac{1}{6}\)

13) \(2x(x - y) - y(y - 2x) = 0\)

Решение: \(2x(x - y) - y(y - 2x) = 2x^2 - 2xy - y^2 + 2xy = 2x^2 - y^2 = 0\) \(2x^2 = y^2\) \(x = \pm \frac{y}{\sqrt{2}}\)

14) \(2xy + 2x(x - y) = 0\)

Решение: \(2xy + 2x(x - y) = 2x(y + x - y) = 2x^2 = 0\) \(x = 0\)

15) \(a(a^2 - 1) + a^2(a - 1) = 0\)

Решение: \(a(a^2 - 1) + a^2(a - 1) = a^3 - a + a^3 - a^2 = 2a^3 - a^2 - a = a(2a^2 - a - 1) = 0\) \(a = 0\) или \(2a^2 - a - 1 = 0\) \(a = 0\) или \(a = \frac{1 \pm \sqrt{1 + 8}}{4}\) \(a = 0\) или \(a = \frac{1 \pm \sqrt{9}}{4}\) \(a = 0\) или \(a = \frac{1 \pm 3}{4}\) \(a = 0\) или \(a = 1\) or