Factorisation using identities is a method for representing a number as a product of two or more factors. These factors can be natural numbers, integers, or eve...
Factorisation using identities is a method for representing a number as a product of two or more factors. These factors can be natural numbers, integers, or even more complex algebraic expressions. By using identities, it is possible to factorise a number in a unique and straightforward way, which can be helpful for solving mathematical problems involving that number.
An identity is a mathematical statement that is true for all values of the variables involved. Factorisation using identities involves applying these identities to rewrite the original expression in a way that makes it easier to factorise. For example, the identity
can be used to factorise the expression
Another identity, the difference of squares formula,
can be used to factorise the expression
These are just a few examples of the many identities that can be used to factorise numbers. By applying these identities creatively, it is often possible to factorise a number in a unique and efficient way.
Moreover, factorisation using identities can also be used to solve mathematical problems involving those numbers. For instance, if you are asked to find the factors of 12, you can factorise 12 as 2 * 2 * 3 * 3, which are the factors of those respective numbers.
Overall, factorisation using identities is a powerful technique that can be used to simplify and solve mathematical expressions involving factors. By understanding and applying these identities, students can gain a deeper understanding of how to factorise numbers and apply this knowledge to solve various mathematical problems