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# TOPIC 2: ALGEBRA ~ MATHEMATICS FORM 2

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### TOPIC 2: ALGEBRA ~ MATHEMATICS FORM 2

Once we learn some of the ātricksā 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,*,āand so on or by
words.
Performing Binary Operations
Perform binary operations
Example 1
Evaluate:
solution
Example 2
Find
solution
Example 3
Solve
Example 4
evaluate,
Example 5
Calculate
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).
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
Example 13
factorize 3x2Ā ā 2xĀ ā 8 by splitting the middle term.
Solution
Example 14
factorize x2Ā + 10x + 25 by splitting the middle term.
Factorization by Inspection
Example 15
factorize x2Ā + 3xĀ + 2 by inspection.
Example 16
factorize 4x2Ā + 5xĀ ā 6 by inspection.

Exercise 1

Factorization Exercise;

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