Question

What is the simplified form of the given expression?
$x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2+3x^3+4y^2+6xy+7x^{3}y+8y^2$

• A. $x^{3}y+11x^2{y}^2+3x{y}^3$
  $+3x^3+4y^2+6xy+8y^2$
• B. $x^{3}y+11x^2{y}^2+3x{y}^3$
  $+3x^3+12y^2+6xy+7x^{3}y$
• C. $8x^{3}y+11x^2{y}^2+3x{y}^3$
  $+3x^3+12y^2+6xy$
• D. $8x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2$
  $+3x^3+12y^2+6xy$

Answer 1

The correct option is C $8x^{3}y+11x^2{y}^2+3x{y}^3$

$+3x^3+12y^2+6xy$
$x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2+3x^3+4y^2$
$+6xy+7x^{3}y+8y^2$ is the given expression.
Now, $x^{3}y$ and $7x^{3}y$ are like terms. Hence they can be added to give
$8x^{3}y$.
Similarly, $4x^2{y}^2$ and $7x^2{y}^2$ are like terms.
They can be added to give $11x^2{y}^2$.
Also, $4y^2$ and $8y^2$ are like terms.
They can be added to give $12y^2$.
Thus, the final simplified expression is
$8x^{3}y+11x^2{y}^2+3x{y}^3+3x^3+12y^2+6xy$.