Question

Using suitable identities find:
i) $(1092{)}^2$
ii) $194\times 206$
iii) $(95{)}^2$

Answer 1

Identities

$(a+b{)}^2=a^2+2ab+b^2$

$a^2-b^2=(a+b)(a-b)$

$(a-b{)}^2=a^2-2ab+b^2$

$\left(1\right)$ $(1092{)}^2=(1000+92{)}^2$

$=(1000{)}^2+2\times 1000\times 92+(92{)}^2$

$=1000000+184000+8464$

$=1,192,464$.

$\left(2\right)$ $194\times 206$

$=(200-6)(200+6)$

$=(200{)}^2-(6{)}^2$

$=40000-36=39964$

$\left(3\right)$ $(95{)}^2$

$=(100-5{)}^2$

$=(100{)}^2-2\times 100\times 5+(5{)}^2$

$=10000-1000+25$

$=9025$.