How to do factorise ? What is Factorise ? Give me some examples ,please . Thank you !
x^2+x-4
(x-2)(x+2)
x^2-2x-15
(x+3)(-5)
Factorising is the process of breaking down an algebraic expression or number into its factors. Factors are the numbers or expressions that, when multiplied together, give the original expression or number. This is useful because it allows us to simplify and solve equations.
To factorise an algebraic expression, follow these steps:
1. Identify if the expression has any common factors. Look for any numbers or variables that can be factored out. For example, in the expression 2x + 4, the common factor is 2.
2. Use factoring techniques depending on the type of expression. Some common techniques include:
- Grouping: When an expression has four or more terms, you can group them together and look for common factors within each group.
- Difference of squares: This is applicable when you have an expression in the form of a^2 - b^2. It can be factored as (a + b)(a - b).
- Perfect square trinomial: If you have an expression in the form of a^2 + 2ab + b^2 or a^2 - 2ab + b^2, it can be factored as (a + b)^2 or (a - b)^2.
- Quadratic trinomial: For expressions in the form of ax^2 + bx + c, you can factorise them using various methods, such as trial and error, completing the square, or using the quadratic formula.
3. Continue factoring until the expression cannot be simplified further.
Here are a few examples of factorising different types of expressions:
1. Factorise 2x + 4:
- Identify the common factor, which is 2: 2(x + 2)
2. Factorise x^2 - 4:
- This is a difference of squares, so it can be factored as (x + 2)(x - 2)
3. Factorise 9x^2 - 16:
- This is also a difference of squares: (3x + 4)(3x - 4)
4. Factorise 4x^2 + 12x + 9:
- This is a perfect square trinomial: (2x + 3)(2x + 3), or (2x + 3)^2
Remember, practice is key to mastering factorising. Try doing more examples and explore different techniques for different types of expressions.