Question

Use the identity you created in the last term item to factor a⁴+9a²+81

Answer 1

`a^4+9a^2+81`
`\begin{gathered} We\text{ can stil express the expressiona as} \\ a^4+(a^2*3^2)+3^4 \\ \end{gathered}`
`x^4+x^2y^2+y^4=\text{ }(x^6-y^6)/(x^2-y^2)`
`\begin{gathered} =((x^2)^3-(y^2)^3)/(x^2-y^2) \\ =((a^2)^3-(3^2)^3)/(a^2-3^2) \end{gathered}`
`\begin{gathered} \\ =\frac{a^6-3^6^{}}{a^2-3^2} \\ =((a^3-3^3)(a^3+3^3))/((a-3)(a+3)) \end{gathered}`
`(a^2+3a+9)(a^2-3a+9)`