Question

expand the following:-. ( 1/2x + 2/3y ) whole sq. 2​

Answer 1

$\textbf{Given:}$

$\mathsf{\left(\dfrac{1}{2x}+\dfrac{2}{3y}\right)^2}$

$\textbf{To expand:}$

$\mathsf{\left(\dfrac{1}{2x}+\dfrac{2}{3y}\right)^2}$

$\textbf{Solution:}$

$\textbf{Identity used:}$

$\boxed{\begin{minipage}{5cm} \\\mathsf{\;\;\;\;(a+b)^=a^2+2\,ab+b^2}\\ \end{minipage}}$

$\mathsf{Consider,}$

$\mathsf{\left(\dfrac{1}{2x}+\dfrac{2}{3y}\right)^2}$

$\textsf{Using the above identity,}$

$\mathsf{=\left(\dfrac{1}{2x}\right)^2+2{\times}\dfrac{1}{2x}{\times}\dfrac{2}{3y}+\left(\dfrac{2}{3y}\right)^2}$

$\mathsf{=\left(\dfrac{1}{2x}\right)^2+\dfrac{1}{x}{\times}\dfrac{2}{3y}+\left(\dfrac{2}{3y}\right)^2}$

$\mathsf{=\dfrac{1}{4x^2}+\dfrac{2}{3xy}+\dfrac{4}{9y^2}}$

$\implies\boxed{\mathsf{\left(\dfrac{1}{2x}+\dfrac{2}{3y}\right)^2=\dfrac{1}{4x^2}+\dfrac{2}{3xy}+\dfrac{4}{9y^2}}}$

$\textbf{Find more:}$

Factorise: -

x^8+x^4/16+1/256

https://brainly.in/question/17290261

Answer 2

$( \frac{1}{2} x + \frac{2}{3} y) {}^{2} \\ \\ = > ( \frac{1}{2} x) {}^{2} + ( \frac{2}{3} y ) {}^{2} + 2 \times \frac{1}{2} x \times \frac{2}{3} y \\ \\ = > \frac{1}{4} x {}^{2} + \frac{4}{9} y {}^{2} + \frac{2}{3} xy$