Multiple choice

Is the following equation a quadratic equation? $(x + 2)^3 = x^3 - 4$

  1. Yes

  2. No

  3. Ambiguous

  4. Data insufficient
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Expanding (x+2)^3 gives x^3 + 6x^2 + 12x + 8. The equation becomes x^3 + 6x^2 + 12x + 8 = x^3 - 4. Subtracting x^3 from both sides results in 6x^2 + 12x + 12 = 0, which is a quadratic equation.

AI explanation

Expand the left side using the algebraic identity (a + b)^3 = a^3 + b^3 + 3ab(a + b), which gives x^3 + 6x^2 + 12x + 8. Setting this equal to the right side gives x^3 + 6x^2 + 12x + 8 = x^3 - 4. Subtracting x^3 from both sides and simplifying yields 6x^2 + 12x + 12 = 0, which is a polynomial of degree 2. Therefore, the answer is Yes.

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