Question

$(x+y{)}^2$ would be equivalent to

• A. $x^2+y^2$
• B. $x^2+y^2+2xy$
• C. $x^2-y^2$
• D. $x^2+y^2-2xy$

Answer 1

The correct option is B $x^2+y^2+2xy$

$(x+y{)}^2$ can be expanded using Distributive property as:
$(x+y{)}^2=(x+y\left)\right(x+y)$
$=x(x+y)+y(x+y)$
$=\underset{–}{x(x+y)}+\underset{–}{y(x+y)}$

$=x^{1+1}+xy+xy+y^{1+1}$ ($\because a^m\times a^n=a^{m+n}$)

$=x^2+\underset{–}{xy+xy}+y^2$
$=x^2+2xy+y^2$

$(x+y{)}^2=x^2+y^2+2xy$

$(x+y{)}^2$ would be equivalent to $x^2+y^2+2xy$.
Therefore, option (b.) is the correct answer.