012. Разложите на множители: а) $$ x^{3}-x^{2} y-x+y ; $$ б) $$ 4 a-a b^{2}+4 b-b^{3} $$ в) $$ p^{3}-p k^{2}-3 k^{2}+3 p^{2} $$ г) $$ b c^{2}-2 c^{2}-b^{3}+2 b^{2} $$

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012. Разложите на множители:

**а)** $$ x^{3} - x^{2} y - x + y $$

$$
x^{3} - x^{2} y - x + y = (x^{3} - x^{2} y) - (x - y) = x^{2}(x - y) -1(x - y) = (x^{2} -1)(x - y) = (x - 1)(x + 1)(x - y)
$$

**Ответ:** $$ (x - 1)(x + 1)(x - y) $$

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**б)** $$ 4a - a b^{2} + 4b - b^{3} $$

$$
4a - a b^{2} + 4b - b^{3} = -b^{3} - a b^{2} + 4a + 4b = -b^{2}(b + a) + 4(b + a) = (4 - b^{2})(a + b) = (2 - b)(2 + b)(a + b)
$$

**Ответ:** $$ (2 - b)(2 + b)(a + b) $$

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**в)** $$ p^{3} - p k^{2} - 3k^{2} + 3p^{2} $$

$$
p^{3} - p k^{2} - 3k^{2} + 3p^{2} = p^{2}(p + 3) - k^{2}(p + 3) = (p^{2} - k^{2})(p + 3) = (p - k)(p + k)(p + 3)
$$

**Ответ:** $$ (p - k)(p + k)(p + 3) $$

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**г)** $$ b c^{2} - 2c^{2} - b^{3} + 2b^{2} $$

$$
b c^{2} - 2c^{2} - b^{3} + 2b^{2} = c^{2}(b - 2) - b^{2}(b - 2) = (c^{2} - b^{2})(b - 2) = (c - b)(c + b)(b - 2) = (b - c)(b + c)(b - 2)
$$

**Ответ:** $$ (b - c)(b + c)(b - 2) $$
012. Разложите на множители: **а)** $$ x^{3} - x^{2} y - x + y = (x - 1)(x + 1)(x - y) $$ **б)** $$ 4a - a b^{2} + 4b - b^{3} = (2 - b)(2 + b)(a + b) $$ **в)** $$ p^{3} - p k^{2} - 3k^{2} + 3p^{2} = (p - k)(p + k)(p + 3) $$ **г)** $$ b c^{2} - 2c^{2} - b^{3} + 2b^{2} = (b - c)(b + c)(b - 2) $$

Разложите на множители:
а)
б)
в)
г)

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