<s>[INST] How can we factorize $a{b^2} + {a^2}b + {a^2}c + a{c^2} + {b^2}c + b{c^2} + 2abc$? How can we factorize $a{b^2} + {a^2}b + {a^2}c + a{c^2} + {b^2}c + b{c^2} + 2abc$?
 [/INST] The factorization of $ab^2+a^2b+a^2c+ac^2+b^2c+bc^2+2abc$
is $(a + b) (a + c) (b + c)$.
First, take out the $(a+b)$ (because a and b are factors to exactly half of the polynomial):
$$((a^2b+a^2c+ac^2+abc)+(ab^2+b^2c+bc^2+abc))*(\frac{a+b}{a+b})$$Then we have:$$(a+b)(ab+ac+bc+c^2)$$Then take out $(a+c)$:$$(a+b)(a(b+c)+c(b+c))$$And voila! By the commutative property, we have: $$(a+b)(a+c)(b+c)$$
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