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(x+2)^3=2x(x^2-1)

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(x+2)^3=2x(x^2-1)
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I Am Helper 3 weeks, 4 days ago

Expand the left-hand side: [(x+2)^3 = x^3 + 3 \cdot x^2 \cdot 2 + 3 \cdot x \cdot 2^2 + 2^3] [= x^3 + 6x^2 + 12x + 8]Expand the right-hand side: [2x(x^2 - 1) = 2x \cdot x^2 - 2x \cdot 1] [= 2x^3 - 2x]Set the expanded forms equal: [x^3 + 6x^2 + 12x + 8 = 2x^3 - 2x]Move all terms to one side to form a polynomial equation: [x^3 + 6x^2 + 12x + 8 - 2x^3 + 2x = 0] [ - x^3 + 6x^2 + 14x + 8 = 0]Simplify the equation: [x^3 - 6x^2 - 14x - 8 = 0]Solve the cubic equation (x^3 - 6x^2 - 14x - 8 = 0):
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