Complete the following example using Nityasam. c (i)(5 x+2 y)^3=(… - Vidyadip

Question

Complete the following example using Nityasam.
$\begin{array}{c}(i)(5 x+2 y)^3=(5 x)^3+(2 y)^3+3(5 x)(2 y)(\_\_\_\_\_\_) \\ =\_\_\_\_\_\_+8 y^3+30 x y(5 x+2 y) \\ =125 x^3+\_\_\_\_\_\_+150 x^2 y+\_\_\_\_\_\_\end{array}$
$\begin{array}{c}(ii) 108 \times 92=(100+\_\_\_\_\_\_)\left(100-\_\_\_\_\_\_\right) \\ =(100)^2-(\_\_\_\_\_\_)^2 \\ =\_\_\_\_\_\_-\_\_\_\_\_\_\\=9936\end{array}$

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Answer

$\begin{array}{c}(i)(5 x+2 y)^3=(5 x)^3+(2 y)^3+3(5 x)(2 y)(5 x+2 y) \\ =125 x^3+8 y^3+30 x y(5 x+2 y) \\ =125 x^3+8 y^3+150 x^2 y+60 x y^2\end{array}$
$\begin{array} {c}(ii)108 \times 92=(100+8)(100-8) \\ =(100)^2-(8)^2 \\ =10000-64 \\ =9936\end{array}$

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