Question

Factor: 81x^6 - 25y^10

Answer 1

=(9x3)2-(5y5)2
=(9x3-5y5)(9x3+5y5)

Answer 2

The factors are, $81 x^{6} - 25 y^{10} = (9x^{3} +5y^{5})(9x^{3} - 5y^{5})$

Given: $81 x^{6} - 25 y^{10}$

To find: To factorize  $81 x^{6} - 25 y^{10}$

Solution:

$81 x^{6} - 25 y^{10} = (9x^{3} )^{2} - (5y^{5})^{2}$

Using the identity,

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

Here $a= 9x^{3} \\b= 5y^{5}$

Therefore,

$81 x^{6} - 25 y^{10} = (9x^{3} + 5y^{5}) (9x^{3} - 5y^{5})$

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