Question

geometrical proof of (a-b)^3

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

This can also be written as:

= (a + b) (a + b) (a + b) 

Now, multiply first two binomials as shown below: 

= { a(a + b) + b(a + b) } (a + b) 

= { a2 + ab + ab + b2 } (a + b) 

On rearranging the terms in curly braces we get: 

= { a2 + b2 + ab + ab } (a + b) 

= { a2 + b2 + 2ab } (a + b) 

Now, multiply trinomial with binomial as shown below: 

= a2(a + b) + b2(a + b) + 2ab(a + b) 

= a3 + a2b + ab2 + b3 + 2ab(a + b) 

= a3 + b3 + a2b + ab2 + 2ab(a + b) 

= a3 + b3 + a2b + ab2 + 2ab(a + b) 

Take ab common from the above red highlighted terms and we get: 

= a3 + b3 + ab(a + b) + 2ab(a + b) 

On adding like terms and we get: 

= a3 + b3 + 3ab(a + b) 

On solving it further we get: 

a3 + b3 + 3a2b + 3ab2 

Hence, in this way we obtain the identity i.e. (a + b)3 = a3 + b3 + 3ab(a + b) = a3 + b3+ 3a2b + 3ab2