The correct option is A (a^x + b^x) (a^x b^x) Formula used: x^2 y^2=(x+y)(x y) nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; nb ...

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Division of Polynomials

Factorise: ...

Question

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

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

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

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

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

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Solution

The correct option is A $(a^{x} + b^{x}) (a^{x} - b^{x})$
Formula used: $x^{2} - y^{2} = (x + y) (x - y)$ (i)
Now, $a^{2 x} - b^{2 x} = (a^{x})^{2} - (b^{x})^{2}$
$= (a^{x} + b^{x}) (a^{x} - b^{x})$ (by (i))
Hence, Option A is correct.

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