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Write $$2ab^3 + a^2c^2 + b^2c^2 - a^2b^2 - 2abc^2 - b^4$$ as a product of linear factors
Correct Answer: 0
PLACEHOLDER ANSWER - the answer is a factorisation, not a number. Group the terms with $$c^2$$, giving $$c^2(a^2 - 2ab + b^2) = c^2(a - b)^2$$. The remaining terms are $$-a^2b^2 + 2ab^3 - b^4 = -b^2(a - b)^2$$. So the expression is $$(a - b)^2(c^2 - b^2) = (a - b)(a - b)(c - b)(c + b)$$.
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