Question

verify the x power3+y power3= (x+y) (x power2-xy+ypower2)​

Answer 1

Answer:

see below

Step-by-step explanation:

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.

Answer 2

Answer:

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