Factorisation using Identities
Factorisation using identities
When dealing with expressions, you might have observed that the form of the expressions we encounter are often repetitive. There are a good number of expressions which have a standard form of factorisation which have been proven over time. These
(a + b)(a – b) =
Therefore, if the expression at hand, has a form that fits the RHS of any one of these identities, then the expression corresponding to the LHS of the identity is the desired factorisation.
Example 4: Factorise
- The above is in the form of the identity:
where a and b are two integers. - We see that a = x while b =
- Thus, the factorised form =
- Which gives us the above factorised answer
Example 5: Factorise
- The above is in the form of the identity:
where a and b are two integers. - We see that a =
while b = 3 - Thus, the factorised form =
- Which gives us the above factorised answer
Example 6: Factorise
- The above is in the form of the identity:
where a and b are two integers. - We see that a =
while b = 6 - Thus, the factorised form =
- Which gives us the above factorised answer
Example 7: Factorise
- In the above expression: the first three terms are in the form of the identity:
where a and b are two integers. - Factorising the first three terms, we get:
- The resulting expression is in the form:
where a and b are random integers (not the ones mentioned in the current problem). - Thus, the resulting factorised form becomes
- Which gives us the above factorised answer
Example 8: Factorise
- Notice that:
m 4 = m 2 2 squared. - Thus, the above expression is in the form of the identity:
where a and b are two integers. - Doing this, we get:
- We see that the expression
m 2 − 16 - Thus, the resulting factorised form becomes
- Which gives us the above factorised answer