What is factor (a+b+c)(ab+ac+bc)-abc ?

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

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factor (a+b+c)(ab+ac+bc)-abc

factor

(a + b + c) (ab + a c + b c) - ab c

a^{2} b + a^{2} c + a b^{2} + a c^{2} + 2 ab c + b c^{2} + b^{2} c

Solution steps

(a + b + c) (ab + a c + b c) - ab c

Expand

(a + b + c) (ab + a c + b c) : a^{2} b + a b^{2} + a^{2} c + 3 ab c + a c^{2} + b^{2} c + b c^{2}

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

Simplify

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

= a^{2} b + a^{2} c + a b^{2} + a c^{2} + 2 ab c + b c^{2} + b^{2} c

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