Question

x^4-y^4. factorise using identity a^2-b^2​

Answer 1

Answer:

Given that,

x^4-y^4x

4

−y

4

To find,

Factors of the given expression

Solution,

We know that, a^2-b^2=(a-b)(a+b)a

2

−b

2

=(a−b)(a+b)

It means,

x^4-y^4=(x^2)^2-(y^2)^2x

4

−y

4

=(x

2

)

2

−(y

2

)

2

Now using the above identity, we get :

(x^2)^2-(y^2)^2=(x^2+y^2)(x^2-y^2)(x

2

)

2

−(y

2

)

2

=(x

2

+y

2

)(x

2

−y

2

)

Again using the above idenity, in (x^2-y^2)(x

2

−y

2

) .

So,

(x^2-y^2)=(x-y)(x+y)(x

2

−y

2

)=(x−y)(x+y)

It would mean that,

x^4-y^4=(x^2+y^2)(x-y)(x+y)x

4

−y

4

=(x

2

+y

2

)(x−y)(x+y) are the factors of the given expression.

Answer 2

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