Question

find the square using suitable identity (product rules) i} (999)^2

Answer 1

$$\begin{gathered} {\left(999\right)}^2 \\ ={\left(1000-1\right)}^2 \\ ={\left(1000\right)}^2+{\left(1\right)}^2-2\left(1000\right)\left(1\right)\left[\mathbf{as}\mathbf{,}\mathbf{}{\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathbf{b}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}\mathbf{2}\mathbf{ab}\right] \\ =1000000+1-2000 \\ =998001 \end{gathered}$$