Chapter 1.5, Problem 54PPE

To determine

The value of the expression $\left(2-3m^2\right)\left(-5\right)$ using Distributive Property.

Answer to Problem 54PPE

  $-10+15m^2$

Explanation of Solution

Given information:

The expression: $\left(2-3m^2\right)\left(-5\right)$ .

Concept Used:

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 $\left(2-3m^2\right)\left(-5\right)$ , first use the right distributive property and then simplify further by combining the like terms as shown below,

  $\begin{array}{c}\left(2-3m^2\right)\left(-5\right)=2\cdot \left(-5\right)-3m^2\cdot \left(-5\right)\\ =-10+15m^2\end{array}$

Thus, the given expression simplifies to $-10+15m^2$ .