Chapter 42, Problem 1A

Add $\left(9x^{2}y+xy-5x{y}^2\right),\left(-3x^{2}y-4xy+5x{y}^2\right)$ and $\left(7x^{2}y+3xy\right)$

To determine

The sum of the given term.

Answer to Problem 1A

  $\left({\text{9x}}^{\text{2}}\text{y}\text{+}\text{xy}-5{\text{xy}}^2\right)+\left(-3{\text{x}}^{\text{2}}\text{y}-4\text{xy}+5{\text{xy}}^2\right)+\left(7{\text{x}}^{\text{2}}\text{y}+\text{3xy}\right)$ is equal to $13{\text{x}}^{\text{2}}\text{y}$.

Explanation of Solution

Given terms:

  $\left({\text{9x}}^{\text{2}}\text{y}\text{+}\text{xy}-5{\text{xy}}^2\right),\left(-3{\text{x}}^{\text{2}}\text{y}-4\text{xy}+5{\text{xy}}^2\right),\left(7{\text{x}}^{\text{2}}\text{y}+\text{3xy}\right)$

Calculation:

Now,

We need to perform addition.

This is done by adding like terms.

  $\begin{array}{l}\Rightarrow \left({\text{9x}}^{\text{2}}\text{y}\text{+}\text{xy}-5{\text{xy}}^2\right)+\left(-3{\text{x}}^{\text{2}}\text{y}-4\text{xy}+5{\text{xy}}^2\right)+\left(7{\text{x}}^{\text{2}}\text{y}+\text{3xy}\right)\\ \Rightarrow {\text{9x}}^{\text{2}}\text{y}\text{+}\text{xy}-5{\text{xy}}^2-3{\text{x}}^{\text{2}}\text{y}-4\text{xy}+5{\text{xy}}^2+7{\text{x}}^{\text{2}}\text{y}+\text{3xy}\text{=}13{\text{x}}^{\text{2}}\text{y}\end{array}$

Thus, $\left({\text{9x}}^{\text{2}}\text{y}\text{+}\text{xy}-5{\text{xy}}^2\right),\left(-3{\text{x}}^{\text{2}}\text{y}-4\text{xy}+5{\text{xy}}^2\right),\left(7{\text{x}}^{\text{2}}\text{y}+\text{3xy}\right)$ is equal to $13{\text{x}}^{\text{2}}\text{y}$.