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Popular >

simplify (a+b+c)^5-a^5-b^5-c^5

Solution

simplify

(a + b + c)^{5} - a^{5} - b^{5} - c^{5}

Solution

5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

Solution steps

(a + b + c)^{5} - a^{5} - b^{5} - c^{5}

(a + b + c)^{5} = (a + b + c) (a + b + c) (a + b + c) (a + b + c) (a + b + c)

= (a + b + c) (a + b + c) (a + b + c) (a + b + c) (a + b + c) - a^{5} - b^{5} - c^{5}

Expand

(a + b + c) (a + b + c) (a + b + c) (a + b + c) (a + b + c) : a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

= a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c - a^{5} - b^{5} - c^{5}

Simplify

a^{5} + 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + b^{5} + c^{5} + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c - a^{5} - b^{5} - c^{5} : 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

= 5 a^{4} b + 5 a^{4} c + 10 a^{3} b^{2} + 10 a^{3} c^{2} + 20 a^{3} b c + 10 a^{2} b^{3} + 10 a^{2} c^{3} + 30 a^{2} b c^{2} + 30 a^{2} b^{2} c + 5 a b^{4} + 5 a c^{4} + 20 ab c^{3} + 30 a b^{2} c^{2} + 20 a b^{3} c + 5 b c^{4} + 10 b^{2} c^{3} + 10 b^{3} c^{2} + 5 b^{4} c

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Frequently Asked Questions (FAQ)

What is (a+b+c)^5-a^5-b^5-c^5 ?
The solution to (a+b+c)^5-a^5-b^5-c^5 is