**3.1 Algebraic Expressions II**

3.1.1 Algebraic terms in Two or More Unknowns

3.1.1 Algebraic terms in Two or More Unknowns

**1.**An

**algebraic term**in two or more unknowns is the product of the unknowns with a number.

*Example 1:*4

*a*^{3}*b*= 4 ×*a*×*a*×*a*×*b***The**

2.

2.

**coefficient**of an unknown in the given algebraic term is the factor of the unknown.

*Example 2:*7

*ab*: Coefficient of*ab*is 7.**are algebraic terms with the same unknowns.**

3. Like algebraic terms

3. Like algebraic terms

**3.1.2 Multiplication and Division of Two or More Algebraic Terms**

The coefficients and the unknowns of algebraic terms can be multiplied or divided altogether.

Example 3:Example 3:

Calculate the product of each of the following pairs of algebraic terms.

(a) 5

*ac*× 2*bc*^{}(b)

**–6***xy*× 5*yz*
$\text{(c)}20xy\times \left(-\frac{2}{5}{x}^{2}y\right)$

Solution:Solution:

**(a)**

5

*ac*× 2*bc*= 5 ×*a*×*c*× 2 ×*b*×*c*= 10*abc*^{2}

(b)

(b)

–6

*xy*× 5*yz*= –6 ×*x*×*y*× 5 ×*y*×*z*= –30*xy*^{2}*z***(c)**

$\begin{array}{l}20xy\times \left(-\frac{2}{5}{x}^{2}y\right)\\ ={\overline{)20}}^{4}xy\times \left(-\frac{2}{\overline{)5}}\right)\times x\times x\times y\\ =-8{x}^{3}{y}^{2}\end{array}$

Example 4:Example 4:

Find the quotients of each of the following pairs of algebraic terms.

$\begin{array}{l}\text{(a)}\frac{42xyz}{7xy}\\ \text{(b)}\frac{12x{y}^{2}}{18xy}\end{array}$

$\text{(c)}35{p}^{2}q{r}^{2}\xf730pr$

Solution:Solution:

$\begin{array}{l}\text{(a)}\frac{42xyz}{7xy}\\ =\frac{{\overline{)42}}^{6}\overline{)x}\times \overline{)y}\times z}{\overline{)7}\overline{)x}\times \overline{)y}}=6z\end{array}$

$\begin{array}{l}\text{(b)}\frac{12x{y}^{2}}{18xy}\\ =\frac{{\overline{)12}}^{2}\overline{)x}\times \overline{)y}\times y}{{\overline{)18}}^{3}\overline{)x}\times \overline{)y}}=\frac{2}{3}y\end{array}$

$\begin{array}{l}\text{(c)}35{p}^{2}q{r}^{2}\xf730pr\\ =\frac{{\overline{)35}}^{7}\overline{)p}\times p\times q\times \overline{)r}\times r}{{\overline{)30}}^{6}\overline{)p}\times \overline{)r}}\\ =\frac{7}{6}pqr\end{array}$

**3.1.3 Algebraic Expressions**

An

**algebraic expression**contains one or more algebraic terms. These terms are separated by a plus or minus sign.

Example 5:Example 5:

7 – 6

*a*^{2}*b*+*c*is an algebraic expression with 3 terms.**3.1.4 Computation Involving Algebraic Expressions**

Computation Involving Algebraic Expressions:

**(a)**2(3

*a*– 4) = 6

*a*– 8

**(b)**(15

*a*– 9

*b*) ÷ 3 = 5

*a*– 3

*b*

**(c)**(6

*a*– 2) – (9 + 4

*a*)

= 6

*a*– 4*a*– 2 – 9= 2

*a*– 11**(d)**(

*a*

^{2}

*b*– 5

*ab*

^{2}) – (6

*a*

^{2}

*b*– 4

*abc*– 6

*ab*

^{2})

=

*a*^{2}*b*– 6*a*^{2}*b*– 5*ab*^{2 }– (– 6*ab*^{2}) – (– 4*abc*)= –5

*a*^{2}*b*+*ab*^{2}+ 4*abc*