Question

x^3=16x
Find all real solutions

Answer 1

x^3 - 16x = 0

x(x^2 - 16) = 0

this equation is true when x = 0 or when x^2 = 16

solutions: x = -4, 0, 4

Answer 2

\(\bf x^3=16x\implies x^3-16x=0\quad \textit{taking common factor}\\ \quad \\
x(x^2-16)=0\implies x(x^2-4^2)=0\qquad\\ \textit{recall that }\color{blue}{a^2-b^2 = (a-b)(a+b)}\\ \quad \\
x(x^2-4^2)=0\implies x(x-4)(x+4)=0\)