Chapter 1.5, Problem 63PPE

To determine

To simplify the expression $5z^2+3z+8z^2$ . If not possible, write simplified.

Answer to Problem 63PPE

  $13z^2+3z$

Explanation of Solution

Given information:

The expression: $5z^2+3z+8z^2$ .

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 simplify the given expression $5z^2+3z+8z^2$ , observe that both terms $5z^2,\text{ and }8z^2$ have the same variable with similar exponents on it, so these are like terms and can be combined as

  $\begin{array}{c}5z^2+3z+8z^2=\left(5z^2+8z^2\right)+3z\\ =\left(5+8\right)z^2+3z\\ =13z^2+3z\end{array}$

Thus, the given expression simplifies to $13z^2+3z$ .