Question

verify X3 - y3 is equal to in bracket x minus y in bracket x power 2 + X Y + Y power 2 and solve 64a power 3 minus 3 4 3 b power 3
​

Answer 1

Answer:

To prove: x

3

−y

3

=(x−y)(x

2

+xy+y

2

)

Consider the right hand side (RHS) and expand it as follows:

(x−y)(x

2

+xy+y

2

)=x

3

+x

2

y+xy

2

−yx

2

−xy

2

−y

3

=(x

3

−y

3

)+(x

2

y+xy

2

+x

2

y−xy

2

)=x

3

−y

3

=LHS

Hence proved.

Yes, we can call it as an identity: For example:

Let us take x=2 and y=1 in x

3

−y

3

=(x−y)(x

2

+xy+y

2

) then the LHS and RHS will be equal as shown below:

2

3

−1

3

=7 and

(2−1)(2

2

+(2×1)+1

2

)=1(5+2)=1×7=7

Therefore, LHS=RHS

Hence, x

3

−y

3

=(x−y)(x

2

+xy+y

2

) can be used as an identity.