Question

Using identities, evaluate $297x303$.

Answer 1

To Evaluate : $297x303$

$297$ can be written as $(300–3)$ and $303$ can be written as $(300+3)$

$297x303=(300–3)\times (300+3)$

Using the identity

$(a+b)(a–b)=a^2–b^2$

$$\begin{gathered} (300–3)\times (300+3)={\left(300\right)}^2–\left(3\right){}^2 \\ (300–3)\times (300+3)={300}^2–3^2 \\ (300–3)\times (300+3)=90000–9 \\ (300–3)\times (300+3)=89991 \end{gathered}$$

$\therefore 297x303=89991$

Hence the result is $89991$