Question

using suitable identity find
102×105​

Answer 1

$\star \; {\underline{\boxed{\pmb{\orange{\frak{ \; Given \; :- }}}}}}$

• 102 × 105

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$\star \; {\underline{\boxed{\pmb{\color{darkblue}{\frak{ \; To \; Find \; :- }}}}}}$

• Solve it using suitable identity

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$\star \; {\underline{\boxed{\pmb{\pink{\frak{ \; SolutioN \; :- }}}}}}$

$\maltese$ Identity Used :

• ${\underline{\boxed{\sf{ \bigg( x + a \bigg) + \bigg( x + b \bigg) = {x}^{2} + \bigg( a + b \bigg)x + \bigg( a \times b \bigg) }}}}$

$\maltese$ First, let's Spilt the given Equation :

$\begin{gathered} \qquad \; \implies \; \; \sf { 102 \times 105 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \implies \; \; {\underline{\boxed{\pmb{\sf{ \bigg( 100 + 2 \bigg) \times \bigg( 100 + 5 \bigg) }}}}} \; {\red{\bigstar}} \\ \\ \\ \end{gathered}$

$\maltese$ Let's Solve the Equation :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg( 100 + 2 \bigg) \times \bigg( 100 + 5 \bigg) } \\ \\ \\ \end{gathered}$

• Applying the Identity :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {100}^{2} + \bigg\{ \bigg( 2 + 5 \bigg) \times 100 \bigg\} + \bigg( 2 \times 5 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { {100}^{2} + \bigg( 7 \times 100 \bigg) + \bigg( 2 \times 5 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 10000 + 700 + 10 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ 10710 }}}}} \; {\purple{\bigstar}} \\ \\ \\ \end{gathered}$

$\therefore \;$ The required answer is 10710 .

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