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(A) To determine if the equation $(x+2)^{3} = x(x^{2}-1)$ is quadratic,we expand both sides.Using the identity $(a+b)^{3} = a^{3} + b^{3} + 3ab(a+b)$,

Vedclass · Accepted Answer

Yes,it is a quadratic equation.

Vedclass · Answer

(A) To determine if the equation $(x+2)^{3} = x(x^{2}-1)$ is quadratic,we expand both sides.Using the identity $(a+b)^{3} = a^{3} + b^{3} + 3ab(a+b)$,the left side becomes:$(x+2)^{3} = x^{3} + 2^{3} + 3(x)(2)(x+2) = x^{3} + 8 + 6x(x+2) = x^{3} + 8 + 6x^{2} + 12x$.The right side is:$x(x^{2}-1) = x^{3} - x$.Equating both sides:$x^{3} + 6x^{2} + 12x + 8 = x^{3} - x$.Subtracting $x^{3}$ from both sides:$6x^{2} + 12x + 8 = -x$.Rearranging the terms to the form $ax^{2} + bx + c = 0$:$6x^{2} + 13x + 8 = 0$.Since this equation is of the form $ax^{2} + bx + c = 0$ where $a 
eq 0$,it is a quadratic equation.

Examine whether the following equation is quadratic or not: $(x+2)^{3} = x(x^{2}-1)$

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