Chapter 1.3, Problem 46PPSE

Solution

To state: The simplified form of the expression $-a^2+2b^2+\frac{1}{4}{a}^2$ by combining like terms.

The resultant answer is $-\frac{3}{4}{a}^2+2b^2$ .

Given information:

The given expression is $-a^2+2b^2+\frac{1}{4}{a}^2$ .

Explanation:

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

Now consider the given expression $-a^2+2b^2+\frac{1}{4}{a}^2$:

Identify the like terms,

  $-a^2+2b^2+\frac{1}{4}{a}^2$

Use Commutative property of addition,

  $-a^2+\frac{1}{4}{a}^2+2b^2$

Use Distributive property,

  $\left(-1+\frac{1}{4}\right)a^2+2b^2$

Combine the like terms,

  $-\frac{3}{4}{a}^2+2b^2$

Therefore, $-\frac{3}{4}{a}^2+2b^2$ is the resultant form of the expression $-a^2+2b^2+\frac{1}{4}{a}^2$ .