Get the information you need quickly and easily with IDNLearn.com. Our experts provide accurate and detailed responses to help you navigate any topic or issue with confidence.
Sagot :
To solve this question we will use the following properties:
[tex]\begin{gathered} a^2-b^2=(a+b)(a-b), \\ (ab)^n=a^{\text{n}}b^n\text{.} \end{gathered}[/tex]Factoring u² we get:
[tex]u^2y^4-81u^2=u^2(y^4-81)\text{.}[/tex]Now, notice that:
[tex]\begin{gathered} y^4=(y^2)^2, \\ 81^{}=9^2\text{.} \end{gathered}[/tex]Substituting the above results in u²(y⁴-81) we get:
[tex]u^2((y^2)^2-9^2)\text{.}[/tex]Using the first property we get:
[tex]u^2(y^2+9)(y^2-9)[/tex]Now, notice that 9=3², therefore:
[tex]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{.}[/tex]Answer:
[tex]u^2(y^2+9)(y^{}+3)(y-3)\text{.}[/tex]
Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.
