Question 709935
{{{x^3-4x=0}}}
Factor. First the greatest common factor of x:
{{{x(x^2-4)=0}}}
The second factor is a difference of squares and can be factored using the pattern, {{{a^2-b^2 = (a+b)(a-b)}}}, with the "a" being "x" and the "b" being "2":
{{{x(x+2)(x-2)=0}}}<br>
Next we use the Zero Product Property which tells us that this product can be zero <i>only</i> if one (or more) of the factors is zero. So:
x = 0 or x+2 = 0 or x-2 = 0
Solving these we get:
x = 0 or x = -2 or x = 2