Chapter 6.1, Problem 29WE

To determine

To calculate: The value of xfrom the expression $cx+dx=c^2-d^2$.

Answer to Problem 29WE

The value of x is $c-d$.

Explanation of Solution

Given information:

The expression $cx+dx=c^2-d^2$.

Formula used:

To solve for x , put all the terms with x on one side and other terms on other side and then factorize both sides, if possible to solve for x and get its value.

Calculation:

Consider the expression $cx+dx=c^2-d^2$.

Recall that to solve for x , put all the terms with x on one side and other terms on other side and then factorize both sides, if possible to solve for x and get its value.

So, take out x common from left-hand side and factorize right-hand side using $X^2-Y^2=\left(X+Y\right)\left(X-Y\right)$.

  $\begin{array}{c}cx+dx=c^2-d^2\\ x\left(c+d\right)=\left(c+d\right)\left(c-d\right)\end{array}$

Now, divide both sides by the coefficient of x as,

  $\begin{array}{c}\frac{x\left(c+d\right)}{\left(c+d\right)}=\frac{\left(c+d\right)\left(c-d\right)}{\left(c+d\right)}\\ x=c-d\end{array}$

Thus, the value of x is $c-d$.