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Solving Secondary 1 Algebraic Manipulation Problems: 5 Helpful Techniques

Algebraic Manipulation

We all know that Mathematics can be an exciting and challenging subject that requires problem-solving skills, logic, and creativity. However, when it comes to algebraic manipulation, many students find it intimidating and overwhelming. Algebraic manipulation is one of the topics covered in Secondary 1 Mathematics, and it involves simplifying, factorising, or expanding algebraic expressions to solve complex problems.

But don't worry, we have got you covered! In this article, we will share with you five effective techniques that will help your child tackle algebraic manipulation questions with ease and confidence. These techniques will not only make solving these problems more manageable, but they will also help your child take their algebraic manipulation skills to the next level.

So, if you want your child to score in Secondary 1 Mathematics this article is a must-read. Let's dive in and discover the five helpful techniques shared by our educator to help your child master algebraic manipulation and excel in this topic!

1. Identifying Like Terms and Unlike Terms in an Algebraic Expression

Identifying Like Terms and Unlike Terms in an Algebraic Expression

Finding terms that are the same and terms that are different is important in algebraic expressions because it helps students simplify and work with these expressions more easily.

For example

2g - 4h - g + 7h = g + 3h. 2g and g are like terms and they can be simplified by taking 2g - g =g, and 4h and 7h are like terms which can be simplified into 7h - 4h = 3h. However, g and 3h are unlike terms. Hence, they cannot be simplified further.


  1. Simplify Like Terms by combining terms with the same variables and degree through adding or subtracting their coefficients.

  2. Unlike Terms cannot be simplified by adding or subtracting their coefficients.

2. Multiplication and Division

When multiplying or dividing algebraic expressions, coefficients and variables are multiplied or divided on their own by applying commutative law. They are not affected by like or unlike terms. The end result does not contain the multiply or divide signs.

Below is an example

multiplying or dividing algebraic expressions

3. Expand Algebraic Expression by Using the Distributive Law (“Rainbow method”)

The Distributive Law is a fundamental concept in algebra that allows us to expand algebraic expressions. This law states that when we multiply a term or a factor to a bracket containing two or more terms, we can distribute the multiplication to each term within the bracket.

This method of expanding algebraic expressions is commonly referred to as the "Rainbow method," as we multiply each term in the bracket by the factor or term outside the bracket, and then write the resulting terms in a rainbow-like pattern.

Distributive Method

For example

Consider the expression 3(x + 2). To expand this expression using the Distributive Law, we multiply the 3 to both terms inside the bracket, giving us 3x + 6.

The Rainbow method is a simple and intuitive way to apply the Distributive Law, and it is an essential tool for any student studying algebra.

4. Factorisation of Algebraic Expression

Factorization is a crucial concept in algebraic manipulation because it allows us to simplify and solve algebraic expressions more easily. Factorisation involves breaking down a complicated expression into simpler parts, by identifying and extracting common factors.

To completely factorise an algebraic expression, it is important to factor out the greatest common factor. By identifying the greatest common factor and dividing each term by it, we can write the expression as a product of the greatest common factor and the quotient of each term divided by the greatest common factor. This makes the expression simpler and easier to work with, and allows us to identify solutions or patterns that may not be obvious in the original form.

5. Orders of Operations

The order of operations is a set of rules that tell you how to do maths operations in a mathematical expression. It's important to know the order of operations to make sure that expressions are always and correctly evaluated.


  1. In the process of simplifying algebraic expressions, the orders of operations have to be followed closely.

  2. The orders of operations are as follows:

    1. Perform operations inside the brackets first

    2. Perform all exponentiations (including roots and powers)

    3. Multiplication and division (from left to right)

    4. Addition and subtraction (from left to right)

In conclusion, algebraic manipulation can be a challenging subject for many Secondary students. However, with the right techniques and strategies, it can be mastered with ease and confidence. This article has provided five helpful techniques that can help students simplify and solve algebraic expressions more efficiently.

These techniques include identifying like and unlike terms, applying the commutative law in multiplication and division, using the distributive law to expand algebraic expressions, factoring expressions by extracting common factors, and following the orders of operations to correctly evaluate expressions. By mastering these techniques, students can develop a strong foundation in algebraic manipulation and succeed in their future studies.

two secondary students enrolled in Secondary Math programme

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