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

The solution to expand (a-b+c)^3 is a^3-3a^2b+3a^2c+3ac^2-3bc^2+3ab^2+c^3+3b^2c-6abc-b^3

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expand (a-b+c)^3

expand

(a - b + c)^{3}

a^{3} - 3 a^{2} b + 3 a^{2} c + 3 a c^{2} - 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c - 6 ab c - b^{3}

Solution steps

(a - b + c)^{3}

Simplify

(a - b + c)^{3} : (a - b + c) (a - b + c) (a - b + c)

= (a - b + c) (a - b + c) (a - b + c)

Expand

(a - b + c) (a - b + c) : a^{2} - 2 ab + 2 a c + b^{2} - 2 b c + c^{2}

= (a^{2} - 2 ab + 2 a c + b^{2} - 2 b c + c^{2}) (a - b + c)

Distribute parentheses

= a^{2} a + a^{2} (- b) + a^{2} c - 2 aba - 2 ab (- b) - 2 ab c + 2 a c a + 2 a c (- b) + 2 a cc + b^{2} a + b^{2} (- b) + b^{2} c - 2 b c a - 2 b c (- b) - 2 b cc + c^{2} a + c^{2} (- b) + c^{2} c

Simplify

a^{2} a + a^{2} (- b) + a^{2} c - 2 aba - 2 ab (- b) - 2 ab c + 2 a c a + 2 a c (- b) + 2 a cc + b^{2} a + b^{2} (- b) + b^{2} c - 2 b c a - 2 b c (- b) - 2 b cc + c^{2} a + c^{2} (- b) + c^{2} c : a^{3} - 3 a^{2} b + 3 a^{2} c + 3 a c^{2} - 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c - 6 ab c - b^{3}

= a^{3} - 3 a^{2} b + 3 a^{2} c + 3 a c^{2} - 3 b c^{2} + 3 a b^{2} + c^{3} + 3 b^{2} c - 6 ab c - b^{3}

125 b^{3} + 216 y^{3}

(\frac{- 3 a ^{3}}{b})^{3}

p^{3} - 3 p^{2} + 3 p - 1

4 x - 2 y + 6

8 (a + b)^{4} + (a + b)

What is expand (a-b+c)^3 ?
The solution to expand (a-b+c)^3 is a^3-3a^2b+3a^2c+3ac^2-3bc^2+3ab^2+c^3+3b^2c-6abc-b^3