Algebra is an essential part of GCSE Maths. However, with practice and an understanding of the main topics, you can become proficient in algebra and succeed in your exams. Remember to simplify expressions, solve equations, factorise expressions, expand brackets, and solve quadratic equations.
Algebra is essential to GCSE Mathematics and can seem quite challenging at first. However, with some practice and understanding, you can become proficient in algebra and succeed in your exams. In this extended explanation, we will cover the main topics of algebra you will encounter in your GCSE Mathematics course.
Simplifying expressions
The first topic in algebra is simplifying expressions. Simplifying expressions means simplifying or reducing the terms and coefficients of an expression to its simplest form. For example, suppose we have an expression 4x + 6x + 2. To simplify this expression, we can combine terms, which are terms that have the same variable and exponent, and add their coefficients.
Therefore, 4x + 6x = 10x. The simplified expression is then 10x + 2.
Another example is 3x + 2y + 5x - y. Here, we can combine like terms 3x + 5x = 8x and 2y - y = y.
The simplified expression is 8x + y.
Solving equations
The third topic in algebra is factorising expressions. Factorising expressions means writing an expression as a product of its factors. For example, consider the expression 2x + 4. We can factorise this expression by taking out the common factor of 2, which gives us 2(x + 2).
Another example is the expression 3x² + 6x. We can factorise this expression by taking out the common factor of 3x, which gives us 3x(x + 2).
Expanding brackets
The fourth topic in algebra is expanding brackets. Expanding brackets means multiplying out the terms inside the brackets. For example, consider the expression 2(x + 3). To expand the brackets, we multiply 2 by each term inside the brackets, which gives us 2x + 6.
Another example is the expression (x + 2)(x + 3). We use the FOIL method to expand the brackets, which are First, Outer, Inner, and Last. First, we multiply the first terms of each bracket, which gives us x².
Then, we multiply the outer terms, which gives us 3x. Next, we multiply the inner terms, which gives us 2x. Finally, we multiply the last terms, which gives us 6. We then combine like terms to get the simplified expression x² + 5x + 6.
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