Chapter 4.3, Problem 3MRE

To determine

To simplify the expression

  $3p^2+4q^2-2p^{2}q-q^2$

Answer to Problem 3MRE

  $3p^2+4q^2-2p^{2}q-q^2=p^2\left(3-q\right)+3q^2$

Explanation of Solution

Given:

  $3p^2+4q^2-2p^{2}q-q^2$

Concept Used:

• If an expression contains more than one operation between its terms and brackets, first solve the terms inside brackets and then apply division followed by multiplication, addition and subtraction.

Calculation:

To simplify the expression

  $3p^2+4q^2-2p^{2}q-q^2$

First, group like terms together.

As,

  $\begin{array}{c}3p^2+4q^2-2p^{2}q-q^2=3p^2-2p^{2}q+4q^2-q^2\\ =3p^2-2p^{2}q+\left(4-1\right)q^2\\ =3p^2-2p^{2}q+3q^2\end{array}$

Now, take $p^2$ common from first two terms, as

  $3p^2-2p^{2}q+3q^2=p^2\left(3-q\right)+3q^2$

Now, above expression can’t be simplified further.

Thus, simplified form of given expression is

  $3p^2+4q^2-2p^{2}q-q^2=p^2\left(3-q\right)+3q^2$