Question

$\text{Use a suitable identity and simplify}{x}^2+6x+9.$

• A. $(x+3{)}^2$
• B. $(x-3{)}^2$
• C. $(x+6{)}^2$
• D. $(x+9{)}^2$

Answer 1

The correct option is A $(x+3{)}^2$

$\text{Given expression:}{x}^2+6x+9$

$\text{We know that,}(a+b{)}^2=a^2+2ab+b^2.$

$\text{On comparing,}{a}^2+2ab+b^2\text{with}{x}^2+6x+9,\text{we have,}{x}^2+6x+9=x^2+2\left(3\right)x+3^2.$

$\text{Hence,}a=x,b=3.$
$\text{So,}{x}^2+6x+9=(x+3{)}^2$.