Chapter 1.5, Problem 69PPE

To determine

To write an algebraic expression for the given verbal expression and then simplify.

Answer to Problem 69PPE

  $5m^2+\left(m^2+5\right)=6m^2+5$

Explanation of Solution

Given information:

The product of 5 and m squared, increased by the sum of the square of m and 5.

Concept Used:

• Like terms are the terms that contain the same variable with similar exponents on it. Constants are like terms as well.

Distributive property:

• Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$
• Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to write an algebraic expression for the given verbal expression, observe that the product of 5 and m squared, that is, $5\cdot m^2$ , is increased by the sum of the squared of m and 5, that is, $m^2+5$ . So, in algebraic expression, it can be written as

  $\begin{array}{c}5\cdot m^2\text{ increased by }\left(m^2+5\right)\\ =5m^2+\left(m^2+5\right)\end{array}$

Now, to simplify further combine the like terms as shown below,

  $\begin{array}{c}5m^2+\left(m^2+5\right)=5m^2+m^2+5\\ =\left(5+1\right)m^2+5\\ =6m^2+5\end{array}$

Thus, the algebraic expression for the given verbal expression is $5m^2+\left(m^2+5\right)$ and simplify to $6m^2+5$ .