The polynomial expression is [tex]$B=6 n^{3}[/tex] ; where, [tex]\quad n \neq 0[/tex].
What is Polynomial expression?
Given:
[tex]$\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$[/tex]
To find:
the value of B is a polynomial expression.
Step 1
Let, [tex]$\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$[/tex]
[tex]$\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}=1$[/tex]
Simplifying the above equation as
[tex]$\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}: \frac{B}{6 n^{3}}$[/tex]
then, we get
[tex]$\frac{B}{6 n^{3}}=1$[/tex]
Step 2
Multiply both sides by [tex]$6 n^{3}$[/tex], then we get
[tex]$\frac{B}{6 n^{3}} \cdot 6 n^{3}=1 \cdot 6 n^{3} $[/tex] where, [tex]\quad n \neq 0[/tex]
Simplifying the equation as
[tex]$B=6 n^{3}[/tex] ; where, [tex]\quad n \neq 0[/tex]
The value of [tex]$B=6 n^{3}[/tex] ; where, [tex]\quad n \neq 0[/tex].
Therefore, the polynomial expression is [tex]$B=6 n^{3}[/tex] ; where, [tex]\quad n \neq 0[/tex].
To learn more about polynomial expression
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