Question 14
The algebraic expression $$(a+b+ab+2)^2+(a-ab+2-b)^2-2b^2(1+a^2)$$ reduces to
Solution
Write the first two squares as $$((a+2)+(b+ab))^2$$ and $$((a+2)-(b+ab))^2$$. Their sum is $$2(a+2)^2+2(b+ab)^2$$. Since $$(b+ab)^2=b^2(1+a)^2$$, subtracting $$2b^2(1+a^2)$$ leaves $$2(a+2)^2+4ab^2$$.
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