Question

Factor this question 16x^4-36

Answer 1

$\begin{gathered} \text{One of the special factors is the binomial term} \\ a^2-b^2=(a+b)(a-b) \end{gathered}$

Based on the given that we have, we could say that

$\begin{gathered} a^2=16x^4 \\ b^2=36 \\ \\ \text{Get the square root of both and we get} \\ a^2=16x^4 \\ \sqrt[]{a^2}=\sqrt[]{16x^4} \\ a=4x^2 \\ \\ b^2=36 \\ \sqrt[]{b^2}=\sqrt[]{36} \\ b=6 \end{gathered}$

Substituting a and b we get that

$\begin{gathered} 16x^4-36=(4x^2+6)(4x^2-6) \\ \\ \text{We can further factor this to} \\ (4x^2+6)(4x^2-6)=2\cdot(2x^2+3)\cdot2(2x^2-3) \\ \\ \text{Simplifying it we have} \\ 4(2x^2+3)(2x^2-3) \\ \text{as our factor} \end{gathered}$