Question

Express ${111}^2$ in the form of $(a+b{)}^2$ .

• A. (${100}^2)$ + ($2\times 100\times 11$) + $(11{)}^2$
• B. (${101}^2)$ + ($2\times 100\times 11$) + $(11{)}^2$
• C. (${100}^2)$ + ($1\times 100\times 11$) + $(11{)}^2$
• D. (${10}^2)$ + ($2\times 100\times 11$) + $(111{)}^2$

Answer 1

The correct option is A (${100}^2)$ + ($2\times 100\times 11$) + $(11{)}^2$

$(111{)}^2$ can be written as $(100+11{)}^2$This is of the form $(a+b{)}^2$.
$(a+b{)}^2$ = $a^2$ + 2ab + $b^2$
$\therefore$ $(100+11{)}^2$ = $(100{)}^2$ + ($2\times 100\times 11$) + ${11}^2$
= 10000 + $2\times 1100$ + 121 = 12321