Question

35. Factorise the following expression 81a4 - 625b
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Answer 1

Answer:

$(9 {a}^{2} + 25 {b}^{2} )(3a - 5b)(3a + 5b)$

Step-by-step explanation:

$81 {a}^{4} - 625 {b}^{4} \: \: \: \: = \: \: \: \: {(3a)}^{4} - {(5b)}^{4} \\ \\ \\ \\ = ({(3a)}^{2} + {(5b)}^{2} )( {(3a)}^{2} - {(5b)}^{2} ) \\ \\ = (9 {a}^{2} + 25 {b}^{2} )(3a - 5b)(3a + 5b)$