Chapter SH, Problem 14.6.2EP

To determine

To divide: the given expression

Answer to Problem 14.6.2EP

The required result is $7a+1$

Explanation of Solution

Given: $\left(14ab+2b\right)÷(2b)$

Calculation:

Essential understanding:

To divide a polynomial by a monomial, divide each term of the polynomial by the monomial.

  $\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}$ .

Write the rational expression,

  $\left(14ab+2b\right)÷(2b)=\frac{14ab+2b}{2b}$

Divide each term by ‘ 2b’ .

  $\begin{array}{l}\frac{14ab+2b}{2b}=\frac{14ab}{2b}+\frac{2b}{2b}\\ =\frac{14}{2}\cdot \frac{a}{1}\cdot \frac{b}{b}\text{+}\frac{2}{2}\cdot \frac{b}{b}\text{ (associative property)}\\ \text{ =7}\cdot a\cdot 1+1\cdot 1\text{ (quotient of powers)}\\ =7a+1\text{ (identity)}\end{array}$

Conclusion:Hence, the result is $7a+1$ .