Question

${(x+y)}^2+2(x+y)+1$ is equivalent to

• A. $(x-y+1)(x+y+1)$
• B. $(x-y-1)(x+y+1)$
• C. $(x+y+1)(x+y+1)$
• D. $(x-y-1)(x-y-1)$

Answer 1

The correct option is C $(x+y+1)(x+y+1)$

$(x+y{)}^2+2(x+y)+1$

$=(x+y{)}^2+2(x+y\left)\right(1)+(1{)}^2$

$\because [a^2+2ab+b^2=(a+b{)}^2]$

$=(x+y+1{)}^2$

$=(x+y+1)(x+y+1)$

Option C is correct.