Question

Find 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$$\left[2Marks\right]$

Answer 1

$x^{3}y+4x^2{y}^2+3x{y}^3+7x^2{y}^2+3x^3+4y^2+6xy+7x^{3}y+8y^2$ is the given expression.
Now, $x^{3}y$ and $7x^{3}y$ are like terms.
Hence they can be added to give $8x^{3}y$.$\left[0.5Mark\right]$

Similarly, $4x^2{y}^2$ and $7x^2{y}^2$ are like terms.
They can be added to give $11x^2{y}^2$.$\left[0.5Mark\right]$

Also, $4y^2$ and $8y^2$ are like terms.
They can be added to give $12y^2$.$\left[0.5Mark\right]$

Thus, the final simplified expression is
$8x^{3}y+11x^2{y}^2+3x{y}^3+3x^3+12y^2+6xy$.$\left[0.5Mark\right]$