MULTIPLICATION AND DIVISION OF ALGEBRAIC NUMBERS

74. Examples.

1. Find the product of $6a^2{b}^2$ and $7a{b}^2{c}^3$.

Since the order of the factors is immaterial,

$$\begin{gathered} 6a^2{b}^3\times 7a{b}^2{c}^3\&=6\times 7\times a^2\times a\times b^3\times b^2\times c^3 \\ \&=42a^3{b}^5{c}^3. \end{gathered}$$

2. Find the product of $-3ab$ and $7a{b}^3$.

$$\begin{gathered} -3ab\times 7a{b}^3\&=-3\times 7\times a\times a\times b\times b^3 \\ \&=-21a^2{b}^4. \end{gathered}$$

75. To Find the Product of Simple Expressions

, therefore,

Take the product of the coefficients and the sum of the indices of the like letters.

Exercise 16.

Find the product of:

1. $5a^2$ and $6a^3$.

2. $8ab$ and $5a^3{b}^2$.

3. $9xy$ and $7xy$.

4. $2a^{2}b$ and $a^3{b}^4{c}^2$.

3 a