### MATHEMATICS FORM TWO TOPIC 2:ALGEBRA

Monday, January 16, 2023

FORM TWO
MATHEMATICS
mathematics notes
When we play games with computers we play by running, jumping and or finding secret things. Well, with Algebra we play with letters, numbers and symbols. And we also get to find secret things. Once we learn some of the ‘tricks’ it becomes a fun challenge to work with our skills in solving each puzzle. So, Algebra is all about solving puzzles. In this chapter we are going to learn some of the skills that help in solving mathematics puzzles.

### Binary Operations

The Binary Operations**Performing Binary Operations**

**Example 1**

Evaluate:

solution

solution

**Example 2**

**Find**

solution

Example 3

Solve

**Example 4**

**evaluate,**

**Example 5**

Calculate

**Brackets in Computation**

Brackets are used to group items into brackets and these items inside the brackets are considered as whole. For example,15 ÷(X + 2) ,means that x and 2 are added first and their sum should divide 15. If we are given expression with mixed operations, the following order is used to perform the operations: Brackets (B) are opened (O) first followed by Division (D) then Multiplication (M), Addition (A) and lastly Subtraction (S). Shortly is written as BODMAS.

**Basic Operations Involving Brackets**

**Example 6**

**Simplify the following expressions:**

4 + 2b – (9b ÷3b)

4z – (2x + z)

solution

**Algebraic Expressions Involving the Basic Operations and Brackets**

**Example 7**

**Evaluate the following expressions:**

solution

**Identities**

For example, 3(2y + 3) = 6y + 9, when y = 1, the right hand side (RHS) and the left hand side (LHS) are both equals to 15. If we substitute any other, we obtain the same value on both sides. Therefore the equations which are true for all values of the variables on both sides are called Identities. We can determine whether an equation is an identity or not by showing that an expression on one side is identical to the other expression on the other side.

**Example 8**

**Determine whether or not the following expressions are identities:**

solution

**Quadratic Expressions**

A Quadratic Expression from Two Linear Factors### The General Form of Quadratic Expression

Quadratic expression has the general form of ax2 + bx + c where a ≠ 0 and a is a coefficient of x2 , b is a coefficient of x and c is a constant. its highest power of variable is 2. Examples of quadratic expressions are 2x2 + x + 1, 4y2 + 3, 3z2 – 4z + 1 and so on. In a quadratic expression 3z2 - 4z + 1, a = 3, b = -4 and c = 1. Also in quadratic expression 4y2 + 3, a = 4, b = 0 and c = 3**Example 9**

**If you are told to find the area of a rectangle with a length of 4y + 3 and a width of 2y + 1.**

Solution

**Example 10**

**3x items were bought and each item costs (4x – 3) shillings. Find total amount of money used.**

### Factorization

Linear Expressions**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).

**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).

**Quadratic Expressions**

Factorization by splitting the middle term

**Example 13**

**factorize 3x2 - 2x – 8 by splitting the middle term.**

Solution

**Example 14**

**factorize x2 + 10x + 25 by splitting the middle term.**

Factorization by Inspection

**Example 15**

**factorize x2 + 3x + 2 by inspection.**

**Example 16**

**factorize 4x2 + 5x – 6 by inspection.**

**Exercise 1**

Factorization Exercise;

## No comments: