Question

Factor completely:u^2y^4-81u^2

Answer 1

To solve this question we will use the following properties:

`\begin{gathered} a^2-b^2=(a+b)(a-b), \\ (ab)^n=a^{\text{n}}b^n\text{.} \end{gathered}`

Factoring u² we get:

`u^2y^4-81u^2=u^2(y^4-81)\text{.}`

Now, notice that:

`\begin{gathered} y^4=(y^2)^2, \\ 81^{}=9^2\text{.} \end{gathered}`

Substituting the above results in u²(y⁴-81) we get:

`u^2((y^2)^2-9^2)\text{.}`

Using the first property we get:

`u^2(y^2+9)(y^2-9)`

Now, notice that 9=3², therefore:

`u^2(y^2+9)(y^2-9)=u^2(y^2+9)(y^2-3^2)=u^2(y^2+9)(y^{}+3)(y-3)\text{.}`

Answer:

`u^2(y^2+9)(y^{}+3)(y-3)\text{.}`