Question

Factor.25x^2+9(5x+3) (5x-3)(5ix+3i) (5ix-3i)(5x+3i) (5x-3i)(5x+3i)^2

Answer 1

Let's begin by listing out the information given to us:

`\begin{gathered} 25x^2+9 \\ Using\text{ sum of two squares, we have:} \\ \text{Let }i=-1 \\ a^2+y^2=(a+yi)(a-yi) \\ a^2=25x^2,y^2=9\Rightarrow a=5x,y=3 \\ 25x^2+9=(5x+3i)(5x-3i) \end{gathered}`

To confirm if the answer is correct, we can multiply the earlier answer:

`\begin{gathered} (5x+3i)(5x-3i)=5x(5x-3i)+3i(5x-3i) \\ 25x^2-15i+15i-9i^2 \\ i^2=-1 \\ 25x^2-9(-1)\Rightarrow25x^2+9 \\ 25x^2+9 \end{gathered}`