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Q5.
ExpertverifiedThe Special Product Formula for the “product of the sum and difference of terms” is $\left(A+B\right)\left(AB\right)=\_\_\_\_\_$. So, $\left(5+x\right)\left(5x\right)=\_\_\_\_\_$
The Special Product Formula for the “product of the sum and difference of terms” is $\left(A+B\right)\left(AB\right)={A}^{2}{B}^{2}$. So, $\left(5+x\right)\left(5x\right)=25{x}^{2}$
If A and B are any real numbers or algebraic expressions, then
$\left(A+B\right)\left(AB\right)={A}^{2}{B}^{2}$
Given $\left(5+x\right)\left(5x\right)$
Here width="82" style="maxwidth: none; verticalalign: 4px;" $A=5,B=x$
Substitute the values in the product of the sum and difference of terms formula to get:
$\begin{array}{l}\left(5+x\right)\left(5x\right)={5}^{2}{x}^{2}\\ \Rightarrow \left(5+x\right)\left(5x\right)=25{x}^{2}\end{array}$
Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree.
Polynomial  Type  Term  Degree 
$\sqrt{2}x\sqrt{3}$ 



Complete the following tables. What happens to the n^{th} root of 2 as n gets larger? What about the nth root of $\frac{1}{2}$?
n  localid="1643113147195" ${\mathbf{2}}^{\frac{\mathbf{1}}{\mathbf{n}}}$  n  ${\left(\frac{1}{2}\right)}^{\frac{\mathbf{1}}{\mathbf{n}}}$ 
1  1  
2  2  
5  5  
10  10  
100  100 
Construct a similar table for ${\mathit{n}}^{\frac{\mathbf{1}}{\mathbf{n}}}$. What happens to the n^{th} root of n as n gets larger?
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