What is expand (x-a^2+2a-3)(x-b^2+2b-3)(x-c^2+2c-3) ?

The solution to expand (x-a^2+2a-3)(x-b^2+2b-3)(x-c^2+2c-3) is

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expand (x-a^2+2a-3)(x-b^2+2b-3)(x-c^2+2c-3)

Solution

expand

(x - a^{2} + 2 a - 3) (x - b^{2} + 2 b - 3) (x - c^{2} + 2 c - 3)

Solution

x^{3} - x^{2} c^{2} + 2 x^{2} c - 9 x^{2} + 6 x a^{2} - 3 a^{2} c^{2} + 6 a^{2} c - 9 a^{2} - x^{2} b^{2} - x^{2} a^{2} + x b^{2} c^{2} + 6 x b^{2} + 6 x c^{2} + 27 x - 12 c x + x a^{2} c^{2} + x a^{2} b^{2} - a^{2} b^{2} c^{2} - 3 a^{2} b^{2} + 2 x^{2} b - 12 b x + 6 a^{2} b + 2 a x^{2} - 12 a x + 6 a b^{2} - 12 ab + 6 a c^{2} - 12 a c - 3 b^{2} c^{2} + 6 b^{2} c + 6 b c^{2} - 12 b c - 2 c x b^{2} - 2 c x a^{2} + 2 a^{2} b^{2} c - 2 b x c^{2} + 4 b c x - 2 a^{2} b x - 4 a^{2} b c - 2 a x c^{2} + 4 a c x - 2 a x b^{2} + 2 a b^{2} c^{2} - 4 a b^{2} c + 4 ab x - 4 ab c^{2} + 8 ab c + 18 a - 9 b^{2} + 18 b - 9 c^{2} + 18 c + 2 a^{2} b c^{2} - 27

Solution steps

(x - a^{2} + 2 a - 3) (x - b^{2} + 2 b - 3) (x - c^{2} + 2 c - 3)

Expand

(x - a^{2} + 2 a - 3) (x - b^{2} + 2 b - 3) : x^{2} + 3 a^{2} - x b^{2} - 6 x - x a^{2} + a^{2} b^{2} + 2 b x - 2 a^{2} b + 2 a x - 2 a b^{2} + 4 ab - 6 a + 3 b^{2} - 6 b + 9

= (x^{2} + 3 a^{2} - x b^{2} - 6 x - x a^{2} + a^{2} b^{2} + 2 b x - 2 a^{2} b + 2 a x - 2 a b^{2} + 4 ab - 6 a + 3 b^{2} - 6 b + 9) (x - c^{2} + 2 c - 3)

Distribute parentheses

= x^{2} x + x^{2} (- c^{2}) + x^{2} \cdot 2 c + x^{2} (- 3) + 3 a^{2} x + 3 a^{2} (- c^{2}) + 3 a^{2} \cdot 2 c + 3 a^{2} (- 3) - x b^{2} x - x b^{2} (- c^{2}) - x b^{2} \cdot 2 c - x b^{2} (- 3) - 6 xx - 6 x (- c^{2}) - 6 x \cdot 2 c - 6 x (- 3) - x a^{2} x - x a^{2} (- c^{2}) - x a^{2} \cdot 2 c - x a^{2} (- 3) + a^{2} b^{2} x + a^{2} b^{2} (- c^{2}) + a^{2} b^{2} \cdot 2 c + a^{2} b^{2} (- 3) + 2 b xx + 2 b x (- c^{2}) + 2 b x \cdot 2 c + 2 b x (- 3) - 2 a^{2} b x - 2 a^{2} b (- c^{2}) - 2 a^{2} b \cdot 2 c - 2 a^{2} b (- 3) + 2 a xx + 2 a x (- c^{2}) + 2 a x \cdot 2 c + 2 a x (- 3) - 2 a b^{2} x - 2 a b^{2} (- c^{2}) - 2 a b^{2} \cdot 2 c - 2 a b^{2} (- 3) + 4 ab x + 4 ab (- c^{2}) + 4 ab \cdot 2 c + 4 ab (- 3) - 6 a x - 6 a (- c^{2}) - 6 a \cdot 2 c - 6 a (- 3) + 3 b^{2} x + 3 b^{2} (- c^{2}) + 3 b^{2} \cdot 2 c + 3 b^{2} (- 3) - 6 b x - 6 b (- c^{2}) - 6 b \cdot 2 c - 6 b (- 3) + 9 x + 9 (- c^{2}) + 9 \cdot 2 c + 9 (- 3)

Simplify

x^{2} x + x^{2} (- c^{2}) + x^{2} \cdot 2 c + x^{2} (- 3) + 3 a^{2} x + 3 a^{2} (- c^{2}) + 3 a^{2} \cdot 2 c + 3 a^{2} (- 3) - x b^{2} x - x b^{2} (- c^{2}) - x b^{2} \cdot 2 c - x b^{2} (- 3) - 6 xx - 6 x (- c^{2}) - 6 x \cdot 2 c - 6 x (- 3) - x a^{2} x - x a^{2} (- c^{2}) - x a^{2} \cdot 2 c - x a^{2} (- 3) + a^{2} b^{2} x + a^{2} b^{2} (- c^{2}) + a^{2} b^{2} \cdot 2 c + a^{2} b^{2} (- 3) + 2 b xx + 2 b x (- c^{2}) + 2 b x \cdot 2 c + 2 b x (- 3) - 2 a^{2} b x - 2 a^{2} b (- c^{2}) - 2 a^{2} b \cdot 2 c - 2 a^{2} b (- 3) + 2 a xx + 2 a x (- c^{2}) + 2 a x \cdot 2 c + 2 a x (- 3) - 2 a b^{2} x - 2 a b^{2} (- c^{2}) - 2 a b^{2} \cdot 2 c - 2 a b^{2} (- 3) + 4 ab x + 4 ab (- c^{2}) + 4 ab \cdot 2 c + 4 ab (- 3) - 6 a x - 6 a (- c^{2}) - 6 a \cdot 2 c - 6 a (- 3) + 3 b^{2} x + 3 b^{2} (- c^{2}) + 3 b^{2} \cdot 2 c + 3 b^{2} (- 3) - 6 b x - 6 b (- c^{2}) - 6 b \cdot 2 c - 6 b (- 3) + 9 x + 9 (- c^{2}) + 9 \cdot 2 c + 9 (- 3) : x^{3} - x^{2} c^{2} + 2 x^{2} c - 9 x^{2} + 6 x a^{2} - 3 a^{2} c^{2} + 6 a^{2} c - 9 a^{2} - x^{2} b^{2} - x^{2} a^{2} + x b^{2} c^{2} + 6 x b^{2} + 6 x c^{2} + 27 x - 12 c x + x a^{2} c^{2} + x a^{2} b^{2} - a^{2} b^{2} c^{2} - 3 a^{2} b^{2} + 2 x^{2} b - 12 b x + 6 a^{2} b + 2 a x^{2} - 12 a x + 6 a b^{2} - 12 ab + 6 a c^{2} - 12 a c - 3 b^{2} c^{2} + 6 b^{2} c + 6 b c^{2} - 12 b c - 2 c x b^{2} - 2 c x a^{2} + 2 a^{2} b^{2} c - 2 b x c^{2} + 4 b c x - 2 a^{2} b x - 4 a^{2} b c - 2 a x c^{2} + 4 a c x - 2 a x b^{2} + 2 a b^{2} c^{2} - 4 a b^{2} c + 4 ab x - 4 ab c^{2} + 8 ab c + 18 a - 9 b^{2} + 18 b - 9 c^{2} + 18 c + 2 a^{2} b c^{2} - 27

= x^{3} - x^{2} c^{2} + 2 x^{2} c - 9 x^{2} + 6 x a^{2} - 3 a^{2} c^{2} + 6 a^{2} c - 9 a^{2} - x^{2} b^{2} - x^{2} a^{2} + x b^{2} c^{2} + 6 x b^{2} + 6 x c^{2} + 27 x - 12 c x + x a^{2} c^{2} + x a^{2} b^{2} - a^{2} b^{2} c^{2} - 3 a^{2} b^{2} + 2 x^{2} b - 12 b x + 6 a^{2} b + 2 a x^{2} - 12 a x + 6 a b^{2} - 12 ab + 6 a c^{2} - 12 a c - 3 b^{2} c^{2} + 6 b^{2} c + 6 b c^{2} - 12 b c - 2 c x b^{2} - 2 c x a^{2} + 2 a^{2} b^{2} c - 2 b x c^{2} + 4 b c x - 2 a^{2} b x - 4 a^{2} b c - 2 a x c^{2} + 4 a c x - 2 a x b^{2} + 2 a b^{2} c^{2} - 4 a b^{2} c + 4 ab x - 4 ab c^{2} + 8 ab c + 18 a - 9 b^{2} + 18 b - 9 c^{2} + 18 c + 2 a^{2} b c^{2} - 27

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Frequently Asked Questions (FAQ)

What is expand (x-a^2+2a-3)(x-b^2+2b-3)(x-c^2+2c-3) ?
The solution to expand (x-a^2+2a-3)(x-b^2+2b-3)(x-c^2+2c-3) is