Question

what isthe answer of (197*203)using identity

Answer 1

Here are some identities useful in solving Question like above (one) :

$\bullet \: \rm(a + b)(a + b) = {a}^{2} + 2ab + {b}^{2}\\ \bullet \: \rm (a - b)(a - b) = {a}^{2} - 2ab + {b}^{2} \\ \small\bullet \: \rm (a + x)(a + y) = {(a)}^{2} + (x + y)a + xy \\ \bullet \: \rm (a - b)(a + b) = {(a)}^{2} - {(b)}^{2} \\ \small\bullet \: \rm(a + b)(a + b)(a + b) = {a}^{3} + {b}^{3} + {3a}^{2} b + {3ab}^{2} \\ \small\bullet \: \rm(a - b)(a - b)(a - b) = {a}^{3} - {b}^{3} - 3ab(a - b)$

Now,

• Simplifying the (given) expression as :

$\huge \dag \: \: \: \tt197 \times 203 \\ \\ \large \to \: \sf(200 - 3) \times (200 + 3) \\ \\ \mapsto \text{Here, This expression is in form of }\\ \tt{(a + b)(a - b)}. \\ \\ \hookrightarrow \text{ Thus, } \tt{ {4}^{th} } \text{ identity is applicable, i.e.}\\ \: \: \boxed{ \tt {a}^{2} - {b}^{2} \: \: \: }\\ \\ \Huge \to \: \sf {(200)}^{2} - {(3)}^{2} \\ \\ \Huge \to \: \: \sf40000 - 9 \\ \\ \Huge \to \: \: \sf \red{39991}$

Hence,

• 197 × 203 = 39991