[tex]\bf 3x^4 -24x^2 +48 \impliedby \textit{common factor}
\\\\
3(x^4-8x^2+16)\quad
\begin{cases}
x^4\implies x^{2\cdot 2}\implies (x^2)^2
\\\\
16\implies -4\cdot -4
\\\\
-8\implies -4+(-4)
\end{cases}
\\\\
thus
\\\\
3(x^4-8x^2+16)\implies 3[(x^2)^2-8x^2+16]
\\\\
3[(x^2-4)(x^2-4)]\impliedby 4=2^2
\\\\
3[(x^2-2^2)(x^2-2^2)][/tex]
[tex]\bf -----------------------------\\\\
\textit{now, recall your }\textit{difference of squares}
\\ \quad \\
(a-b)(a+b) = a^2-b^2\qquad \qquad
a^2-b^2 = (a-b)(a+b)\\\\
-----------------------------\\\\
thus
\\\\
3[(x^2-2^2)(x^2-2^2)]
\\\\
3[(x-2)(x+2)(x-2)(x+2)]\implies 3[(x-2)^2(x+2)^2][/tex]
