MATHEMATICS FORM 2 TOPIC 2: ALGEBRA

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MATHEMATICS FORM 2 TOPIC 2: ALGEBRA

ALGEBRA

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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.
The Binary Operations
Describe the binary operations
When two numbers are combined according to the instructions given and produce one number we say that they are binary operations. For example, when we add 4 to 6 we get 10, or when we multiply 4 by 3 we get 12. We see that addition of two numbers lead to one number and multiplication of two numbers produce one number. This is binary operation. The instructions can be given either by symbols like X,*,∇and so on or by words.
Performing Binary Operations
Perform binary operations
Example 1
Evaluate:
ALGEBRA
solution
ALGEBRA
Example 2
Find
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solution
ALGEBRA
Example 3
Solve
ALGEBRA
Example 4
evaluate,
ALGEBRA
Example 5
Calculate
ALGEBRA
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.
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

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.

Factorization by splitting the middle term

ALGEBRA
Example 13
factorize 3x2 – 2x – 8 by splitting the middle term.
Solution
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Example 14
factorize x2 + 10x + 25 by splitting the middle term.
ALGEBRA

Factorization by Inspection

Example 15
factorize x2 + 3x + 2 by inspection.
ALGEBRA
Example 16
factorize 4x2 + 5x – 6 by inspection.
Exercise 1
Factorization Exercise;
ALGEBRA

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