Chapter 8.7, Problem 62PFA

To determine

To find the equivalent expression of $3r^3-7r^2-3r+7.$

Answer to Problem 62PFA

  $(3r-7)(r+1)(r-1)$

Explanation of Solution

Given:

Expression: $3r^3-7r^2-3r+7$

Concept used:

Factorisation by grouping terms is used.

Consider the expression,

  $\Rightarrow 3r^3-7r^2-3r+7$

Combining the like terms,

  $\begin{array}{l}\Rightarrow 3r^3-3r-7r^2+7\\ \Rightarrow 3r(r^2-1)-7(r^2-1)\\ \Rightarrow (3r-7)(r^2-1)\end{array}$

Further, $(r^2-1)$ can be factorised by difference of squares.

  $\begin{array}{l}\Rightarrow (r^2-1)\\ $ \Rightarrow ({(r)}^2-{(1)}^2)$$ \Rightarrow (r+1)(r-1)$\end{array}$

Thus, the expression can be completely factored as,

  $\Rightarrow (3r-7)(r+1)(r-1)$

Conclusion:

Therefore, the expression is equivalent to $(3r-7)(r+1)(r-1)$ .