Question 125

Solve the following:
(a + b + c)(ab + bc + ca) - abc = ?

Solution

(a + b + c)(ab + bc + ca) - abc

= $$a^2b + a^2c + ab^2 + cb^2 + bc^2 + ac^2 + 2abc$$

= $$a^2(b +c)+bc(b+c)+a(b^2+c^2+2bc)$$

= $$a^2(b+c)+bc(b+c)+a(b+c)^2$$

=$$(b+c)(a^2+bc+ab+ac)$$

= (b + c)[a(a + b) + c(a + b)]

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

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Solve the following:(a + b + c)(ab + bc + ca) - abc = ?