Math, asked by Anonymous, 6 months ago

verify 1) x³+y³=(x+y)(x²-xy+y²)
2) x³-y³=(x-y)(x²+xy+y²)
using some non-zero positive integers and check by actual multiplication. can you call these as identities? ​

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Answered by usricharan999
1

Step-by-step explanation:

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Maths

Polynomials

Algebraic Identities

Verify x^3 - y^3 = (x - y)(...

MATHS

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Asked on December 26, 2019 by

Bhavna Tikhade

Verify x

3

−y

3

=(x−y)(x

2

+xy+y

2

) using some non-zero positive integers and check by actual multiplication. Can you call theses as identities?

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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.

Answered by virtsharma876537
1

Answer:

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