Question

factorise x4-y4. solve full using identity (a2-b2)

Answer 1

Answer:

(x+y)(x-y)(x²-y²)

Explanation:

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We know the algebraic identity:

a²-b² = (a+b)(a-b)----(1)

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Factors of x⁴-y⁴

= (x²)²-(y²)²

= (x²-y²)(x²+y²) [from (1)]

= (x-y)(x+y)(x²+y²) [from(1)]

Therefore,

x⁴-y⁴ = (x-y)(x+y)(x²+y²)

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Answer 2

Given that,

$x^4-y^4$

To find,

Factors of the given expression

Solution,

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

It means,

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

Now using the above identity, we get :

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

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

So,

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

It would mean that,

$x^4-y^4=(x^2+y^2)(x-y)(x+y)$ are the factors of the given expression.