**TOPIC 1: EXPONENTS AND RADICALS**

**Exponents**

Re-arranging Letters so that One Letter is the Subject of the Formula

Re-arrange letters so that one letter is the subject of the formula

A formula is a rule which is used to calculate one quantity when other quantities are given. Examples of formulas are:

Example 14

From the following formulas, make the indicated symbol a subject of the formula:

Solution

Transposing a Formulae with Square Roots and Square

Transpose a formulae with square roots and square

Make the indicated symbol a subject of the formula:

Exercise 3

**1**. Change the following formulas by making the given letter as the subject of the formula.

**2**. Use mathematical tables to find square root of each of the following:

Linear Expressions

Factorize linear expressions

The

operation of resolving a quantity into factors, when we expand

expressions, is done by removing the brackets. The reverse operation is

Factorizing and it is done by adding brackets.

operation of resolving a quantity into factors, when we expand

expressions, is done by removing the brackets. The reverse operation is

Factorizing and it is done by adding brackets.

Example 11

Factorize the expression 5a+5b.

**Solution**

In

factorization of 5a+5b, we have to find out a common thing in both

terms. We can see that the expression 5a+5b, have got common coefficient

in both terms, that is 5. So factoring it out we get 5(a+b).

factorization of 5a+5b, we have to find out a common thing in both

terms. We can see that the expression 5a+5b, have got common coefficient

in both terms, that is 5. So factoring it out we get 5(a+b).

Example 12

Factorize 18xyz-24xwz

**Solution**

Factorizing

18xyz-24xwz, we have to find out highest common factor of both terms.

Then factor it out, the answer will be 9xz(2y-3w).

18xyz-24xwz, we have to find out highest common factor of both terms.

Then factor it out, the answer will be 9xz(2y-3w).

Quadratic Expressions

Factorize quadratic expressions

When

we write the quadratic expression as a product of two factors we say

that we have factorized the expression. We are going to learn two

methods used to factorize quadratic expressions. These methods are

factorization by Splitting the middle term and factorization by

Inspection.

we write the quadratic expression as a product of two factors we say

that we have factorized the expression. We are going to learn two

methods used to factorize quadratic expressions. These methods are

factorization by Splitting the middle term and factorization by

Inspection.

**Factorization by splitting the middle term**

Example 13

factorize 3x

^{2}– 2*x*– 8 by splitting the middle term.
Solution

Example 14

factorize x

^{2}+ 10x + 25 by splitting the middle term.**Factorization by Inspection**

Example 15

factorize x

^{2}+ 3*x*+ 2 by inspection.
Example 16

factorize 4x

^{2}+ 5*x*– 6 by inspection.
Exercise 1

Factorization Exercise;

Asanteni sana kwa notes nzuri kazi yenu in nzuri nimeipenda

nice one