Разложить на множители 1) m^3-m-am^2+a 2) ay-2ab+2by-y^2 3) x^2+4yz-xy-4xz 4) ay^2+2a^2-a^3-2y^2 5) a^2+ab+az+bx 6) 6m-12-2n+mn 7) x+y-x^2-xy 8) 4ab^2+4ab+a+ab 9) 5m^2n-6an+10m^2-3an^2 10) 8mn^3-24n^2-7mn+21 11) ax^2+yx^2+ax+cx^2+yx+cx 12) 12a^2y^2-6ayc+3ac^2-6a^2yc-c+2ay

Question

Merkuri

Математика

11 мая, 17:04

Разложить на множители 1) m^3-m-am^2+a 2) ay-2ab+2by-y^2 3) x^2+4yz-xy-4xz 4) ay^2+2a^2-a^3-2y^2 5) a^2+ab+az+bx 6) 6m-12-2n+mn 7) x+y-x^2-xy 8) 4ab^2+4ab+a+ab 9) 5m^2n-6an+10m^2-3an^2 10) 8mn^3-24n^2-7mn+21 11) ax^2+yx^2+ax+cx^2+yx+cx 12) 12a^2y^2-6ayc+3ac^2-6a^2yc-c+2ay

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Роман Николаев · Answer 1

1) m³ - m - am² + a = m * (m² - 1) - a * (m² - 1) = (m² - 1) * (m - a).

2) ay - 2ab + 2by - y² = a * (у - 2b) - y * (y - 2b) = (y - 2b) * (a - y).

3) x² + 4yz - xy - 4xz = x * (x - y) - 4z * (x - y) = (x - y) * (x - 4z).

4) ay² + 2a² - a³ - 2y² = y² * (a - 2) - a² * (a - 2) = (a - 2) * (y² - a²).

5) a² + ab + az + bz = a * (a + z) + b * (a + z) = (a + z) * (a + b).

6) 6m - 12 - 2n + mn = n * (m - 2) + 6 * (m - 2) = (m - 2) * (n + 6).

7) x + y - x² - xy = x * (1 - x) + y * (1 - x) = (1 - x) * (x + y).

8) 4ab² + 4ab + a + ab = a * (4b + 1) + ab * (4b + 1) = (4b + 1) * (a + ab).

9) 5m²n - 6an + 10m² - 3an² = 5m² * (n + 2) - 3n * (n + 2) = (n + 2) * (5m² - 3n).

10) 8mn³ - 24n² - 7mn + 21 = 8n² * (mn - 3) - 7 * (mn - 3) = (mn - 3) * (8n² - 7).

11) ax² + yx² + ax + cx² + yx + cx = ax * (x + 1) + yx * (x + 1) + cx * (x + 1) = (x + 1) * (ax + yx + cx).

12) 12a²y² - 6ayc + 3ac² - 6a²yc - c + 2ay = 6ay * (2ay - c) - 2ac * (2ay - c) + 1 * (2ay - c) = (2ay - c) * (6ay - 2ac + 1).