Question

Translate each sentence into an equation. (Lesson 2-1). (p. 140)

Four times the difference of$b$ and six is equal to$b$ squared.

Short answer

The required equation is $4\left(b-6\right)=b^2$.

Step-by-step solution

Step-1. Apply the concept of sum for unlike terms.

Like terms are the terms having the same variables and being raised to the same index. A coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

For example,$4x$ and$5x$ are like terms.

Unlike terms are the terms not having the same variables and or are raised to a different index.

For example, 4 and$5x$ are unlike terms.

We can subtract like terms by subtracting their coefficients, we cannot subtract the unlike terms.

Now we are given variable$b$ and we subtract 6 from it to obtain

$b-6$

Step 2. Apply the concept of multiplication of a constant and a variable.

When a constant is multiplied by a variable we just append the constant in front of the variable.

We are given a constant $4$and a difference $b-6$, so their product will be$4\left(b-6\right)$

Step-3. Apply the concept of raising variable to an index.

When a variable is multiplied by itself we raise the index/exponent of the variable by two, when it is multiplied once more to this product we raise the index to three.

In this fashion variables are written, for example:

$\begin{array}{l}x\times x=x^2\\ x\times x=x^3\end{array}$

Thus $b^2$is$b$ raised to the second power.

Step 4. Evaluate the two results.

To get the final expression we equate the results of steps 1 and 2 to get:

$4\left(b-6\right)=b^2$

Thus, the required equation is $4\left(b-6\right)=b^2$.