Chapter 6.1, Problem 30WE

To determine

To calculate: The value of x from the expression $ax+bx=a^2+2ab+b^2$.

Answer to Problem 30WE

The value of xis $a+b$.

Explanation of Solution

Given information:

The expression $ax+bx=a^2+2ab+b^2$.

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 $ax+bx=a^2+2ab+b^2$.

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 $X^2+2XY+Y^2={\left(X+Y\right)}^2$.

  $\begin{array}{c}ax+bx=a^2+2ab+b^2\\ x\left(a+b\right)={\left(a+b\right)}^2\end{array}$

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

  $\begin{array}{c}\frac{x\left(a+b\right)}{\left(a+b\right)}=\frac{{\left(a+b\right)}^2}{\left(a+b\right)}\\ x=a+b\end{array}$

Thus, the value of xis $a+b$.