Chapter 1.3, Problem 7LC

Solution

To identify: The error and correct it which is made by a student while simplifying the expression.

  $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)=q^{2}p+3p-5q$

The resultant answer is $5p^{2}q+p-5q$ .

Given information:

The given solution is $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)=q^{2}p+3p-5q$ .

Explanation:

Consider the given solution $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)=q^{2}p+3p-5q$:

It can be seen that the expression is simplified without distributing -1 while combining the like terms.

  $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)$

Substitute the values of variable c as $-5$ into the given expression,

  $5{\left(-5\right)}^3-6{\left(-5\right)}^2-2\left(-5\right)$

Now correct the simplification of $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)=q^{2}p+3p-5q$ ,

  $3p^{2}q+2p-\left(5q+p-2p^{2}q\right)$

Now distribute $-1$ over the brackets

  $3p^{2}q+2p-5q-p+2p^{2}q$

Use Commutative property,

  $3p^{2}q+2p^{2}q+2p-p-5q$

Combine like terms,

  $5p^{2}q+p-5q$

Therefore, the correct simplified form is $5p^{2}q+p-5q$ .