alleryWhich equation appears cubic at first glance but actually simplifies to a quadratic equation?
A$x(x+1)+8=(x+2)(x-2)$
B$x(2x+3)=x^2+1$
C$(x+2)^3=x^3-4$
D$2x^2-3x+1=0$
Answer & Solution
Correct answer: C. $(x+2)^3=x^3-4$
Expanding $(x+2)^3$ gives $x^3+6x^2+12x+8$.
So $(x+2)^3=x^3-4$ becomes $x^3+6x^2+12x+8=x^3-4$, and the $x^3$ terms cancel.
This leaves $6x^2+12x+12=0$, which is quadratic.
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