Algebra factorising is a fundamental skill in mathematics that involves finding the factors of an algebraic expression. It is a helpful technique that can help simplify algebraic expressions and solve equations. In GCSE Mathematics, algebra factorising is an important topic that students must master.
Factorising involves breaking down an algebraic expression into smaller parts or factors. Then, these factors are multiplied together to produce the original expression. The aim is to simplify the expression and make it easier to work with.
For example, let's consider the algebraic expression 2x + 4. We can factorise this expression by finding the common factor of 2:
2x + 4 = 2(x + 2)
In this example, the common factor is 2, and we have factored it out of both terms of the expression. As a result, we have written the expression as a product of 2 and the sum (x + 2). It is called the factorised form of the expression when arranged in this way.
Another example is the algebraic expression x2 - 4. We can factorise this expression using the difference of two squares formula:
x2 - 4 = (x + 2)(x - 2)
In this example, we have used the formula a2 - b2 = (a + b)(a - b) to factorise the expression. We can check that this factorisation is correct by expanding the brackets:
(x + 2)(x - 2) = x2 - 2x + 2x - 4 = x2 - 4
Now, consider a more complex example: 6x2 + 11x - 10. To factorise this expression, we need to find two numbers that multiply to -60 (the product of the coefficients of the x2 and constant terms) and add up to 11 (the coefficient of the x term). These numbers are 15 and -4:
6x2 + 11x - 10 = 6x2 + 15x - 4x - 10
= 3x(2x + 5) - 2(2x + 5)
= (3x - 2)(2x + 5)
In this example, we have used a technique called grouping. We have split the middle term into two terms that add up to the coefficient of the x term. We have then factored out the common factor of (2x + 5) and written the expression as a product of two factors.
Algebra factorising involves breaking down algebraic expressions into smaller parts or factors to simplify them. This can be done using various techniques, such as finding common factors, using the difference of two squares formula, or grouping terms.
Factorising quadratic expressions is a particular type of algebra factorising that involves breaking down expressions with x2 terms. These expressions are usually in the form ax2 + bx + c, where a, b, and c are constants.
To factorise quadratic expressions, we need to find two numbers that will multiply to a × c and add up to b. These two numbers will be the coefficients of the terms in the factorised form of the quadratic expression. We can then write the expression as a product of two factors in the form (mx + p)(nx + q).
