Polynomials


   
 
Factorisation using Identities
 
Recall the following identities for finding the products:
 
 
 
 
 
 
 
Observe that the LHS in the identities are all factors and the RHS are their products. Thus, we can write the factors as follows:
 
 
 
 
 
 
 
From the above identities we observe that a given expression, which is in the form of an identity can be written in terms of its factors.
 
Factorisation using the identity
 
 
which can be reduced to this form. Let us consider some examples.
 
Example 1:
 
 
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Example 2:
 
 
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Factorisation using the identity
 
Example 1:
 
 
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Example 2:
 
 
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Steps for factorisation using identities:
 
Recognise the appropriate identity.
 
Rewrite the given expression in the form of the identity.
 
Write the factors of the given expression using the identity.
 
Factorisation using the identity
 
 
Example 1:
 
 
Suggested answer:
 
 
 
 
 
Example 2:
 
 
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Factorisation using the identity
 
Example 1:
 
 
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Example 2:
 
 
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[Since both are same i.e., 4ab and 4bc are negative, b should be negative]
 
 
Factorisation using the identity
 
Example 1:
 
 
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Here we have x = 2x, y = 3y
 
 
Example 2:
 
 
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Example 3:
 
 
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Here x = 7, y = 2x
 
 
 
Example 4:
 
 
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Here x = 6a, y = 2b
 
 
 
Factorisation using the identity
 
 
 
 
 
 
Let x + y = u
 
 
 
 
Substitute x + y for u,
 
 
 
 
Hence,
 
 
 
 
 
Example 1:
 
 
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Here x = 2a, y = b, z = 3c
 
 
 
 
Example 2:
 
 
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Here x = 2x, y = 5y, z = 1
 
 
 
  
     
   
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