Question

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Answer 1

Answer:

The answer is -

Step-by-step explanation:

To factorize $a^{2x}$ - $b^{2x}$

First take common

That is,

= $1^{x}$($a^{2}$ - $b^{2}$)

Follow the identity $a^{2}$ - $b^{2}$ = (a + b)(a - b)

=  $1^{x}$[(a + b)(a - b)]  

= ($a^{x}$ + $b^{x}$)(($a^{x}$ - $b^{x}$)

Proof

$a^{2x}$ - $b^{2x}$ = ($a^{x}$ + $b^{x}$)(($a^{x}$ - $b^{x}$)

$a^{2x}$ - $b^{2x}$ = $(a^{x})^{2}$ - $(b^{x})^{2}$ [using the identity $a^{2}$ - $b^{2}$ = (a + b)(a - b) = $a^{2x}$ - $b^{2x}$

Hence proved

that

($a^{x}$ + $b^{x}$)($a^{x}$ - $b^{x}$) is correct

HOPE THE ANSWER WILL BE A GREAT PATH OF LEARNING, MATE

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Answer 2

Question :

... Factorization of

${a}^{2x} - {b}^{2x} \: is$

Answer :

${a}^{2x} - {b}^{2x}$

$( {a}^{x)2} - ( {b}^{x)2}$

$by \: using \: {x}^{2} - {y}^{2} = (x + y)(x - y) \\ ( {a}^{x)2} - ( {b}^{x)2} = ( {a}^{x} + {b}^{x} )( {a}^{x} - {b}^{x} )$

I hope it is helpful answer for you.

It is very simple answer by using Algebraic identities.