Math, asked by hazuhazik10, 5 hours ago

2⁴-(x⁴-y⁴) factorise​

Answers

Answered by Hansika4871
0

Given:

An expression 2⁴-(x⁴-y⁴).

To Find:

Simplifying the expression into similar terms.

Solution:

The given question can be solved by using the rationalization formulae.

1. The given expression is 2⁴-(x⁴-y⁴).

2. The expression 2⁴-(x⁴-y⁴) can also be written as,

=> 2⁴-(x⁴-y⁴) = 2⁴-x⁴+ y⁴, ( Solved using the formula (a^2-b^2) = (a+b)(a-b) ).

=> (2⁴-x⁴) + y⁴ = (2^2 + x^2) ( 2^2 - x^2)  +  y⁴,

3. It can be further simplified as,

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

4. The other way of simplifying the same expression is,

=>  2⁴-(x⁴-y⁴) = 2^4 - ( x^2 +y^2) ( x^2-y^2), ( Solved using the same formula (a^2-b^2) = (a+b)(a-b) ).

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

Therefore, the expression 2⁴-(x⁴-y⁴) can be simplified as 2^4 - (x^2+y^2) (x+y) (x-y) and (2+x) (2-x) (2^2 + x^2) +y^4.

Answered by presentmoment
1

=16-(x^{4} +y^{4} )(x^{2} -y^{2} ).

Step-by-step explanation:

x^{4}-y^{4}= (x^{2} +y^{2} )(x^{2}- y^{2} ).

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

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

Here

         2^{4} =(x^{4} -y^{4} )

= 16-(x^{2}+ y^{2} )(x+y)(x-y)

Therefore the Factorise of 2^{4}-(x^{4} -y^{4} )

= 16-(x^{2} +y^{2} ) (x+y)(x-y).

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