Chapter 1.3, Problem 51PPSE

Solution

To state: The simplified form of the expression $\frac{1}{2}\left(x^2-y^2\right)-\frac{5}{2}\left(x^2-y^2\right)$ by combining like terms.

The resultant answer is $-2x^2+2y^2$ .

Given information:

The given expression is $\frac{1}{2}\left(x^2-y^2\right)-\frac{5}{2}\left(x^2-y^2\right)$ .

Explanation:

Like terms are those terms that have same variables raised to the same power.

Now consider the given expression $\frac{1}{2}\left(x^2-y^2\right)-\frac{5}{2}\left(x^2-y^2\right)$:

Identify the like terms,

  $\frac{1}{2}\left(x^2-y^2\right)-\frac{5}{2}\left(x^2-y^2\right)$

Remove the grouping symbol,

  $\frac{1}{2}{x}^2-\frac{1}{2}{y}^2-\frac{5}{2}{x}^2+\frac{5}{2}{y}^2$

Use Commutative property of addition,

  $\frac{1}{2}{x}^2-\frac{5}{2}{x}^2-\frac{1}{2}{y}^2+\frac{5}{2}{y}^2$

Use Distributive property,

  $\left(\frac{1}{2}-\frac{5}{2}\right)x^2+\left(-\frac{1}{2}+\frac{5}{2}\right)y^2$

Combine the like terms,

  $-2x^2+2y^2$

Therefore, $-2x^2+2y^2$ is the resultant form of the expression $\frac{1}{2}\left(x^2-y^2\right)-\frac{5}{2}\left(x^2-y^2\right)$ .